We derive the general cubic action for perturbations about a cosmological background in the quadratic subclass of degenerate higher-order scalar-tensor (DHOST) theories, focusing on scalar-scalar-tensor interactions. We adopt a fully covariant formulation and implement unitary gauge at the level of perturbations. This mixed sector provides the key ingredient for estimating the decay rate of a gravitational wave into two scalar excitations in the quadratic DHOST models of dark energy in the late-time Universe.

Over the past century, both theoretical advancements and experimental observations have established General Relativity (GR) as the most successful framework for describing gravitational phenomena. However, observations from multiple cosmological probes over the last two decades have provided compelling evidence for the accelerated expansion of the Universe. The rapid progress in observational astronomy and precision cosmology has highlighted several challenges that motivate the search for extensions or alternatives to General Relativity. In this thesis, we investigate alternative formulations of gravity based on non-Riemannian geometry, with particular emphasis on (f(Q)) gravity in the presence of bulk viscosity. We first explore the existence of exact cosmological solutions for viscous fluid models within the framework of (f(Q)) gravity and constrain the free parameters of these solutions using observational datasets. The resulting constrained models are then employed to study the evolutionary history of cosmic expansion. Our analysis demonstrates that the proposed viscous (f(Q)) gravity models can successfully account for the observed late-time acceleration of the Universe. Furthermore, we examine several classes of nonlinear viscous (f(Q)) gravity models through both dynamical systems and observational analyses. Particular attention is given to the cosmological viability of these models and their ability to reproduce the different evolutionary epochs of the Universe, ranging from matter-dominated eras to accelerated expansion phases.

In the decay of quantum particles under field theoretic consideration, the decay rate is typically a convolution of the density of modes the primary field is allowed to decay into and the allowed probability density for the field to decay into such modes. In free space, though many such processes show high amplitude of such transitions towards the infrared sector, the depletion of allowed mode density in that regime arrests the efficacy of such decays at low energies. Therefore in free space, in order to enhance the decay rate, one needs the transition probability density to be rich enough towards the high energy sector where mode density support is also high enough to make the rate sufficiently large. In this work we argue that in the controlled boundary condition environment e.g. in a cavity, the mode functions of product field receive significant support towards their infrared sector, boosting the probability (and hence rates) of low energy processes. The cavity geometry offers sweet spots in terms of resonant geometry around which the interaction of a primary field with product fields receives dramatic enhancement, significantly enlarging its decay rates. Therefore, a judicious selection of cavity geometry serves as a potential substitute to studying interesting processes at high energy. The results have direct relevance for the study of QED processes and implications for the study of exotic new physics are also discussed.

We present a pedagogical introduction to the cosmological constant problem that requires only basic knowledge of quantum field theory and general relativity. A massive real scalar field is used to illustrate how the quantum vacuum energy density and pressure can be calculated both in flat spacetime and in an expanding universe. Detailed computations are provided for dimensional, cutoff, and adiabatic regularizations. No attempt is made to address quantum gravitational effects, and the expanding-universe background is treated classically. We point out that although the commonly cited discrepancy of 120 orders of magnitude between theory and observation is based on an estimate that does not account for regularization and renormalization, fundamental principles of quantum field theory nevertheless lead to a huge mismatch. In addition to this large discrepancy, we emphasize that there are also conceptual challenges related to cosmic expansion, such as the choice between comoving and physical scales in certain contexts and the non-uniqueness of vacuum.

This work presents a comprehensive account of a gravitational model based on the gauging of the $\mathrm{ISIM}(2)$ Lorentz subgroup parameters through the so-called soft algebra formalism. After presenting a closed form for $\mathfrak{sim}(2)$ and its inhomogeneous extension, we proceed to develop a complete torsionless gravitational model, culminating in an invariant action.

We investigate a K-essence like cosmological model whose scalar-field potential is constructed from a negative power-law Sáez--Ballester potential. By means of a suitable field redefinition from $\phi$ to $\varphi$, we show that the resulting field equations acquire a mathematical structure analogous to that of a previously solved Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological model. This correspondence allows us to obtain exact classical solutions for both the scale factor and the scalar field within the Hamiltonian formalism. The resulting cosmological dynamics exhibits a late-time accelerated expansion, with the deceleration parameter approaching the asymptotic value $q\rightarrow -1$, characteristic of a de Sitter phase. At the quantum level, the corresponding Wheeler-DeWitt (WDW) equation is derived and exact quantum solutions are obtained. These results provide a consistent classical and quantum description of the cosmological evolution generated by this class of K-essence models. In this formalism, the scalar field remains as a cosmic background where the universe unfolds, which is glimpsed from the quantum solution perspective.

We study the dynamical and scattering properties for the Euler-Heisenberg BH surrounded by perfect fluid dark matter. The geometry contains a compact non-linear electrodynamic correction governed by the EH coupling and a logarithmic dark-matter contribution governed by the surrounding PFDM halo. We study the scalar, electromagnetic and a particular effective axial spin-2 channel constructed on the fixed EH plus PFDM background, acting as a proxy for the gravitational-like perturbation problem and not for the fully coupled gravitational perturbation problem. We compute the quasinormal-mode spectrum employing a thirteenth-order WKB method supplemented with Padé resummation and compare it with the eikonal prediction calculated in terms of the angular frequency of the photon sphere and the Lyapunov exponent. Moreover, we study the near-extremal configurations and derive a purely imaginary branch of quasinormal frequencies in the near-horizon region, whose damping rate increases with the PFDM parameter and is nearly spin-independent. We then compute exact greybody factors by direct numerical integration of the radial wave equation and compare them to analytical lower bounds. We also analyze the absorption cross sections and the Hawking emission spectra. We also calculate the relativistic enhancement of the neutrino-antineutrino annihilation channel outside the EHPFDM black hole. We find that the PFDM parameter contracts the optical structure, increases the oscillation frequency, enhances the damping rate and suppresses transmission. On the other hand, the Euler-Heisenberg correction leads to a weaker near-horizon deformation whose effect becomes relevant for sufficiently large charge. These results provide a common scattering framework for comparing the impact of dark-matter environments and nonlinear electrodynamics

Why do unrelated approaches to quantum gravity nearly all find spacetime two-dimensional at the shortest scales? Each theory answers only within its own dynamics; we highlight a single kinematic route to the same value, one assuming no field equation and living in the geometry of the space of states alone. That route is concentration of measure on the Fubini-Study geometry of pure states, which forces the pairwise distances of a random sample to equalize as the dimension grows, so any finite sample collapses to an equidistant dust whose thresholded metric graph is the complete graph. Handed this dust, a diffusion probe reads it as two-dimensional in the large-sample limit, the value the running spectral dimension takes at the dust's single relaxation scale, a property of the measurement rather than the structure; this convergence on two is not, by itself, evidence that spacetime is two-dimensional. Whether a given two is such an artifact is governed by the Laplacian spectrum near zero, and whether that reading carries across an emergence map is the condition we call spectral faithfulness; a single relaxation scale encodes no spectral dimension that tells one structure from another. The collapse, the probe value, and the eigenvalue-density criterion are machine-checked in Lean 4 against Mathlib, resting on the standard Beta law of overlaps; a power-law tail of small eigenvalues reads a genuine dimension, a single scale above a gap reads two at its own clock, and a gapped two-scale band reads off the universal line. These classes are run on graph-Laplacian proxies, and whether a link-graph reading carries to the physical nonlocal operator is left open. The spectral test reads the eigenvalue density near zero and separates, on a given structure, a measurement artifact from a dimension the structure genuinely expresses.

We present a systematic, model-agnostic analysis of out-of-equilibrium effects, including viscosity and thermal conductivity, in non-radial oscillations of relativistic stars. Extending the Lindblom-Detweiler formalism, we construct, to our knowledge, the first general framework for linear, non-radial relativistic stellar perturbations that incorporates generic nonequilibrium corrections to the perfect-fluid sector in both the even- and odd-parity channels. Our framework is formulated in terms of the tensorial structure and thermodynamic decomposition of generic corrections without relying on any specific constitutive relations, thereby allowing us to elucidate, at a structural level, how these effects enter the perturbation equations and contribute to geometric deformations and fluid fluctuations. As an application, we consider the Bemfica-Disconzi-Noronha-Kovtun fluid and perturbatively investigate shifts in the frequencies and damping times of modes connected to their perfect-fluid counterparts in the limit of vanishing transport coefficients. We also identify structural features of the closed eigenvalue problem that can give rise to additional mode families. Our formalism provides a unified framework for analyzing how different relativistic fluid theories modify the structure of non-radial stellar perturbations.

In this work, we show how simulations performed on classical computers such as those of Numerical Relativity can be tackled by quantum algorithms for solving systems of partial differential equations. We develop a proof-of-principle quantum algorithm for solving Einstein Field Equations in the Wahlquist-Estabrook-Buchman-Bardeen(WEBB) tetrad Numerical Relativity formalism [1], and test it by evolving the Schwarzschild Black Hole spacetime in the WEBB Numerical Relativity formalism [2], perturbing it to obtain gravitational Quasinormal Modes [3]. We program the algorithm components for a gate-based, digital quantum computer using the Qiskit software [4] and run it on classical simulators and physical IBM quantum computers through the UKRI National Quantum Computing Centre (NQCC) Quantum Access program and quantify the computational resources and runtime.

The Unruh effect predicts that accelerated observers perceive the inertial vacuum as populated by particles, providing a flat-spacetime analogue of Hawking radiation. Its direct observation, however, remains experimentally challenging, since an Unruh temperature of $1\,\mathrm{K}$ requires accelerations of order $10^{20}\,\mathrm{m/s^2}$. Here, we show that the Lamb shift of a centripetally accelerated atom inside a high-$Q$ cavity provides a sensitive spectroscopic probe of the Unruh effect at dramatically lower accelerations. The cavity reshapes the electromagnetic density of states and converts otherwise tiny noninertial corrections into tunable level shifts. Depending on the atomic angular velocity and cavity detuning, the Lamb shift can be enhanced, strongly quenched, or completely screened. Remarkably, for experimentally realistic parameters, a rotation-induced shift of order $10\;\mathrm{Hz}$ can arise already at accelerations as low as $0.5\,\mathrm{m/s^2}$, more than twenty orders of magnitude below the acceleration scale conventionally associated with direct Unruh detection. These results identify cavity-controlled Lamb-shift spectroscopy as a viable route toward laboratory tests of the circular Unruh effect in the ultralow-acceleration regime.

Timelike orbits constitute a crucial probe for exploring the intrinsic properties of curved spacetimes, and the carried gravitational radiation signals provide a direct window into strong field gravity. In this paper, we develop a versatile computational framework based on Mathematica and the OpenMP parallel architecture to simulate the rational orbits of timelike particles and their gravitational radiation in static spherically symmetric spacetimes. Specifically, requiring only the user defined covariant metric, this numerical tool can efficiently calculate rational orbits across various configurations, as well as the corresponding gravitational wave polarization states and characteristic strains. The package presented here offers a highly efficient and comprehensive one-stop solution for investigating the properties of curved spacetimes and their potential observational signatures. To demonstrate the reliability and capability of our code, we apply it to the Schwarzschild spacetime as a test case, illustrating the functionality of the code across several key aspects, including the effective potential, stable orbital regions, rational and irrational orbits, and gravitational wave signals. Furthermore, we show that the gravitational waves emitted by an extreme mass ratio inspiral system composed of an intermediate mass black hole and the Galactic Center supermassive black hole have the potential to be identified by future space detectors.

With increasingly large numbers of gravitational-wave events, population inference is now beginning to move beyond predictions of marginal distributions and to probe correlations between compact-binary parameters such as masses, spins, and redshifts. These correlations have strong constraining power for both astrophysics and tests of general relativity. In this paper, we present an idealized analytical model to study the interplay between single-event correlations, systematic biases, and population-level correlations. With this, we investigate the potential emergence of false-positive measurements of population-level correlations. We quantify how the presence of correlations at the single-event level between a pair of parameters increases the uncertainty of population-level correlations for those parameters, potentially obscuring the true underlying population correlation if present. We also find that if waveform systematics lead to biases that are correlated across the catalog (which is likely, because certain regions of the parameter space are more difficult to model), this can be effectively absorbed by a population analysis that targets correlations and can be misinterpreted as such. This simple Gaussian-based model may serve as a broad compass for future, more detailed explorations.

We revisit thawing quintessence models with nearly flat scalar-field potentials using a cosmographic framework. Earlier work indicates that the cosmographic reconstruction of the slope $\lambda=-(dV/d\phi)/V$ of the quintessence potential in the general case requires the knowledge of the cosmographic paremeters up to the jerk parameter $j$. In this work we show that the slow-roll conditions $[(dV/d\phi)/V]^2 \ll 1$ and $|(d^2V/d\phi^2)/V| \ll 1$ allow the reconstruction of the slope of a nearly flat potential with knowledge of only the deceleration parameter $q$ (and the density parameter $\Omega_\phi$). Confronting the assumption of near-flatness with the cosmographic data after DESI DR2, however, reveals possible tension between the two. We further show that these models exhibit attractor behaviour in the $w$--$\Omega_\phi$ and $w$--$w'$ phase planes, corresponding to a universal thawing evolution with $w \approx -1$ at early times. We also derive the corresponding relation in the cosmographic $q$--$j$ plane and show that different cosmological expansion histories can produce the same thawing evolution. Nevertheless, all viable trajectories remain close to the $\Lambda$CDM limit $j=1$.

We reexamine the quantum circuit model of black hole evaporation proposed in Class. Quantum Grav. 35, 235013 (2018). This model incorporates the tripartite systems: black hole, just radiation and early radiation. We apply the scrambling unitary matrix with a single parameter $\theta$ to the ground state of the qubits in infalling matter towards a black hole in order to generate initial qubit states of the black hole that are more general than those in Class. Quantum Grav. 35, 235013 (2018). Specifically, the scrambling unitary matrix reduces to no scrambling and maximum scrambling when $\theta=0$ and $\theta=\pi/2$, respectively. Our aim is to explore the role of quantum monogamy in the firewall formation between the black hole and radiation. In this model, entanglement and firewall formation depend on the black hole mass $M$ and the frequency of Hawking radiation $\omega$. For the initial state with $\theta=\pi/2$, a firewall emerges at an earlier stage of the evolution than with $\theta=0$. We also find that a firewall structure emerges between BH and JR, and that the information is carried away by radiation for all values of $M\omega$, provided that $\theta$ lies within a certain analytically determined range. Following the unitary gate dynamics, the initial black hole qubit state can be retrieved from its imprint on the final radiation state, which was originally hidden behind the black hole's horizon. These results may provide insight into the properties of multipartite entanglement due to the different initial states in the evolution of a quantum circuit model for black hole evaporation.

In this paper, using a novel geometrical approach, we relate the concept of the thermodynamic temperature of the free gravitational field, to the non-affinity of real null geodesics in a Newman Penrose tetrad. This naturally links various temperature functions like Clifton, Ellis and Tavakol temperature, Hawking temperature, Unruh temperature etc., in their respective proper limits. Although our analysis is done within the realm of local rotational symmetry, we show that the result can be extended to other Petrov type D geometries, like the Kerr spacetime. We also obtain the geometrical and causal transport equations for this temperature function, in the form of a hyperbolic wave equation with a forcing term, sourced by Weyl curvature and matter. Finally, as a possible physical interpretation of the non-affinity, we relate the geometrical temperature with the gravitational red/blue shift of light rays travelling along null geodesics.

We study the stability of a generalization of the GHS-GM black hole in the presence of a dilaton and a monopole field. We find that the thermal behaviour of system depends on the scalar charge of the dilaton field and as this parameter is decreasing the system becomes more thermally stable. We also find that, as the charge of the black hole is increasing, both the real and the imaginary parts of the quasi-normal frequencies decrease in absolute value. The overtone modes die out faster than the fundamental modes and no positive imaginary parts appear, indicating the stabilty of the system

We study extreme-mass-ratio inspirals (EMRIs) evolving in a scalar cloud environment that may form through superradiant instabilities, using a fully relativistic perturbative framework that allows for eccentric and inclined orbits. EMRIs, consisting of a stellar-mass compact object inspiraling into a supermassive black hole, are key sources for space-based gravitational-wave detectors such as LISA. Previous relativistic studies of EMRIs in scalar clouds have been restricted to circular, equatorial motion. Here, instead, we focus on a Schwarzschild black hole background to incorporate eccentricity and orbital inclination. By computing the scalar energy and angular momentum scattered off to spatial infinity and absorbed at the event horizon, we show that orbital eccentricity can induce a dense spectrum of resonances near the last stable orbit, associated with strong relativistic apsidal precession. We further find that orbital inclination can significantly modify the orbital energy and angular momentum losses. In particular, we identify a critical inclination angle below which, at sufficiently small orbital radii, there is a net transfer of energy from the scalar cloud to the orbit. Moreover, for sufficiently large eccentricities, resonances associated with relativistic apsidal precession persist across the full range of inclinations, although their structure changes significantly between prograde and retrograde orbits. These results provide a foundation for future studies of EMRIs in scalar cloud environments on fully generic orbits around spinning black holes.

For slowly-varying noise, time-frequency methods offer a natural middle ground between the efficiency of the frequency domain and the generality of the more expensive time domain. Despite growing adoption, such methods remain less well documented and less familiar in the gravitational-wave literature, compared to the ubiquitous frequency domain. Aimed at gravitational-wave analysts, in this paper we present a self-contained account of time-frequency methods, detail derivations for a specific basis, namely the Wilson-Daubechies-Meyer (WDM) basis, and share intuition and lessons learned. We document key concepts: the orthogonality and good time-frequency localization of the basis, the edge effects at the DC and Nyquist frequencies, the forward and inverse transforms and their practical implementation, and the noise covariance matrix and likelihood in the time-frequency domain.

We investigate the head-on coalescence of charged binary black holes in Einstein-Maxwell-Scalar (EMS) theory using numerical relativity. The binaries are built from charged puncture initial data representing two Reissner-Nordström black holes immersed in a purely kinetic scalar perturbation: the scalar field initially vanishes, while its conjugate momentum provides a small seed for the instability. We evolve the coupled gravitational, electromagnetic, and scalar sectors and monitor the apparent horizons, the emitted radiation, and the scalar field on the horizons. Our simulations show that the nonminimal electromagnetic-scalar coupling can dynamically trigger the growth of scalar hair even when the individual black holes are initially scalar-free. The subsequent evolution depends on the coupling strength and on the charge retained by the remnant. For weak coupling, or when charge cancellation suppresses the electromagnetic source after merger, the scalar field is radiated away or absorbed by the final horizon and the system dynamically descalarizes. For sufficiently strong coupling and nonzero remnant charge, the scalar field remains finite and the final black hole approaches a scalarized configuration. The coalescence also excites scalar radiation whose time profile is qualitatively correlated with the dominant gravitational-wave mode during the nonlinear stage of the collision. These results provide a binary realization of scalarization/descalarization transitions in EMS theory and show that the fate of scalar hair is controlled by the interplay between the scalar coupling and the charge content of the remnant.

Many exact solutions of Einstein-Maxwell and Einstein-Maxwell-dilaton theory share a common structural pattern in which the metric functions are built from harmonic functions on a specified spatial base, often taken to be flat. We investigate this pattern by considering the Einstein-Maxwell-dilaton theory in arbitrary dimensions, where the dilaton field is non-trivially coupled to the Maxwell field and to a Liouville-type potential proportional to the cosmological parameter. Without imposing either the base geometry or the harmonic form of the metric function in advance, we show that for the generic branch, the field equations force the dilaton couplings to be equal, restrict the spatial base geometry to be Ricci flat, and make the metric function harmonic on this base. The resulting spacetime can then be written in terms of a conformal potential. We also consider a purely spatial branch, which instead leads to a distinct constraint on the coupling constants. These results provide a unified field-equation derivation of the harmonic behavior and conformal structure that appear in several classes of solutions, including multi-center geometries, cosmological solutions, and dynamical black holes.

The black mirror spacetime proposed by Tzanavaris, Boyle, and Turok [1] connects the two exterior regions of the extended Schwarzschild black hole directly to each other, with no intervening interior region. Using techniques adapted from previous work on signature change, we reexamine the black mirror spacetime as a model of double signature change, and investigate whether there is a surface layer at the horizon, that is, a distributional curvature singularity corresponding to an impulsive gravitational wave. We confirm that the black mirror spacetime does not contain any such singularity, and compare our result with previous claims that the curvature components are analytic. We also discuss the global structure of the black mirror spacetime, and examine what happens to worldlines and curves passing through.

Scalar-induced gravitational waves are usually treated as a classical stochastic background sourced by phase-random curvature perturbations. We show that this description can miss residual quantum information. Starting from a decohered two-mode Gaussian scalar state, we derive explicit transfer relations between the scalar anomalous coherence and the covariance matrix of induced tensor modes. For a localized scalar power spectrum, the ordinary tensor power is sourced by scalar power contractions, whereas the opposite-mode tensor coherence is sourced by scalar anomalous-coherence contractions. This coherence can generate nonzero tensor discord and a connected tensor-power covariance even after scalar entanglement has vanished. We identify the connected covariance and phase-sensitive strain correlations as probes of primordial quantum coherence in secondary gravitational-wave backgrounds, and discuss their possible relevance for future space-based interferometers and pulsar timing arrays.

We investigate late-time cosmology in extended symmetric teleparallel gravity coupled to a Dirac-Born-Infeld (DBI) scalar field within $f(Q,T)$ gravity, where $Q$ is the non-metricity scalar and $T$ is the trace of the matter energy-momentum tensor. Working on a spatially flat Friedmann-Lemaître-Robertson-Walker background and treating the cosmic medium as an effective perfect fluid, we derive the background field equations for $f(Q,T)+\mathrm{DBI}$ gravity and obtain analytic solutions for the linear choice $f(Q,T)=\alpha Q+\beta T$. We then constrain the model parameters with a Markov Chain Monte Carlo analysis using Hubble-rate data, DESI BAO (DR2) measurements, and the Pantheon+SHOES Type~Ia supernova sample. The joint posteriors (Tables II and III) are broadly consistent with current late-time constraints and allow a direct comparison with $\Lambda$CDM, quantifying the departures driven by the $\beta T$ coupling and the DBI sector. Although the model does not reproduce every observational feature exactly, it provides a statistically viable alternative avenue to the standard paradigm and a useful framework for exploring potential remedies to existing tensions, including the $H_0$ discrepancy, without claiming a definitive resolution.

Scalar-induced gravitational waves are usually modeled as a classical stochastic background sourced by primordial curvature perturbations. We investigate whether residual quantum-information properties of the scalar sector can survive decoherence and leave imprints in the induced tensor background. Using the covariance-matrix formalism, we describe primordial curvature perturbations as decohered two-mode squeezed Gaussian states and identify the anomalous scalar coherence that may remain after scalar entanglement has vanished. We then derive the leading scalar-to-tensor transfer relations for opposite-momentum induced tensor modes. The ordinary tensor power is sourced by scalar power contractions, whereas the opposite-mode tensor coherence is sourced by anomalous scalar-coherence contractions. This tensor coherence controls the induced Gaussian discord and generates connected and phase-sensitive observables, including a connected power covariance $\kappa(k)\propto |\gamma_k|^2/\alpha_k^2$. Thus the robust signature is not a universal shift of the gravitational-wave spectrum, but a correlated tensor background with nontrivial covariance and phase structure. We discuss phenomenological templates and provide an illustrative Fisher estimate for future gravitational-wave observations. Our results suggest that scalar-induced gravitational waves may offer a new probe of primordial quantum correlations beyond entanglement.

We present a method for determining the spin parameter $a/M$ and inclination angle $i$ of a non-extremal Kerr black hole from segments of the critical curve identified in black hole images. Although the critical curve itself is not directly observable, higher-order photon rings accumulate near it, and in realistic observations localized portions of the resulting brightness enhancement may be available for identifying segments of the critical curve. We introduce standardized segments of the critical curve and define three observables that characterize their geometry. We show that these observables uniquely determine $(a/M,i)$, together with an auxiliary parameter $r_{nl}\in[0,1]$ specifying the location of the identified segment along the critical curve, within the domain considered. Thus, even a segment of the critical curve contains sufficient geometric information to constrain the black hole spin and inclination without reconstructing the full critical curve. The framework is naturally suited to realistic observations and may be extended to more general rotating black hole spacetimes.

We give a summary of our work [3] and [4] with Geoffrey Compère and this http URL Hoque. After quickly reviewing the $\Lambda$-BMS solution space and why it is not trivial to define an analogue of Bondi mass loss, we discuss how this can be resolved by studying the linearized solutions. Then we describe how to solve the linearized Einstein s equations in the generalized harmonic gauge and the set of assumptions such as adiabaticity and being at a large distance from the source that allows us to write the metric perturbations in terms of the source multipole moments. We point out how to consistently truncate the multipole expansion. We then discuss the net change of the metric perturbation at future infinity due to a source that is time-varying in a finite time interval that will be connected to the memory effect. We explain how to define charge flows using the holographic stress tensor and what form they take in terms of multipole moments at second order in perturbations. We conclude with a some remarks on the results.

In this work, we extend the static spherically symmetric black hole solutions of revised Deser--Woodard (D-W) nonlocal gravity. Due to the linearity of the field equations, we show that the first-order expansion around the Schwarzschild solution is linear in both the temporal metric component and the reciprocal of the radial metric component. Therefore, a mode-by-mode superposition can be properly defined for different types of correction terms. We then further study two additional asymptotically flat extensions, a logarithmically dressed correction and an exponentially suppressed correction. The logarithmically dressed correction gives a slowly decaying deviation from Schwarzschild as the radius becomes large, making it a more extended nonlocal effect, whereas the exponentially suppressed correction is localized near the horizon and shifts the horizon inward for positive correction amplitude. These correction terms are physically motivated by common mechanisms in modified gravity: Logarithmic terms are possibly related to effects of quantum corrections, and exponential terms can arise from finite-range or screened gravitational effects.

Certain torsion scalar invariants are known to diverge at the horizon of the Schwarzschild solution in the Teleparallel Equivalent of General Relativity (TEGR), obstructing its interpretation as a black hole spacetime. We show that Schwarzschild TEGR geometries split into two distinct subclasses determined by the Lorentz sector of the geometry -- the elements of the tetrad and spin connection not encoded in the metric but appearing in the torsion. In the regular subclass, the divergences are absent and the horizon belongs to the manifold, supporting a consistent black hole interpretation. In the singular subclass, the divergences are genuine and the horizon is excluded from the manifold. As part of this analysis, we clarify the role of inertial contributions in teleparallel gravity, showing that the proper frame does not, by itself, eliminate inertial effects and that the horizon singularities are independent of the inertial structure of the frame. Using three independent approaches -- the inertial frame condition, horizon-penetrating coordinates, and the horizon regularity criterion -- we determine the complete class of Lorentz sector functions compatible with a regular horizon in Schwarzschild TEGR geometries. For this class, all torsion scalar invariants remain finite at the horizon and analytic extensions across it are admitted.

We develop a covariant virtual work structure and a corresponding d'Alembert-Lagrange principle for spacetime geometry. Within this framework, General Relativity arises as a particular realization of the principle, leading to a covariant d'Alembert-Lagrange formulation in which the Einstein field equations arise from the vanishing of total covariant virtual work on admissible metric variations, rather than from action extremality. The covariant virtual work structure provides a covariant classification of constraint-induced contributions, distinguishing ideal reactions, which perform no virtual work, from non-ideal sectors contribute explicitly to it. The structure extends naturally to one-sided admissibility conditions, yielding a covariant inequality structure. Constraints generate reaction terms. In particular, an isoperimetric constraint produces a cosmological term as an ideal reaction fixed by spacetime averages, so that the cosmological constant emerges as a global parameter determined by admissibility, reflecting an intrinsically nonlocal geometric origin.

The persistent discrepancy between early-time and late-Universe measurements of the Hubble constant commonly known as the $H_0$ tension remains one of the most pressing open questions in modern cosmology. In this work, we explore whether modifications to the gravitational sector, specifically within the framework of symmetric teleparallel gravity, can offer a viable pathway toward alleviating this tension. We consider two functional forms of $f(Q)$ gravity: a logarithmic model and a nonlinear saturation model, both of which introduce geometric corrections to the standard expansion history without invoking a cosmological constant. Constraining these models through a Bayesian MCMC analysis against a comprehensive suite of observational data, including cosmic chronometers, Type Ia supernova compilations (Pantheon, Pantheon$+$SH0ES, and DES SN5YR), and BAO measurements from SDSS and DESI, we find that both models remain statistically competitive with $\Lambda$CDM. The logarithmic model, in particular, consistently infers intermediate values of $H_0$ between the \textit{Planck} and SH0ES benchmarks across all dataset combinations, and carries lower AIC and BIC penalties, establishing it as the more promising candidate for partially easing the $H_0$ tension within a modified gravity framework.

We investigate the defocusing of null geodesics in dynamical, non-singular black-hole-to-white-hole transitions. Working at the level of spacetime kinematics, and without assuming any specific gravitational field equations, we show that the contraction and disappearance of a trapped region, as well as the subsequent formation and expansion of an anti-trapped region, necessarily require a violation of the null convergence condition. This conclusion follows directly from the behaviour of the null expansions across the trapping and anti-trapping horizons, and is therefore independent of the microscopic mechanism responsible for singularity resolution. We then illustrate this general argument by constructing a class of explicit bouncing geometries in generalised Painlevé-Gullstrand coordinates, obtained by promoting static regular black holes with de Sitter cores to time-dependent black-hole-to-white-hole transition models. For a Bardeen-type mass function, we show that the required violation of the null convergence condition is localised within the intermediate dynamical phase in which the trapped region evaporates and the anti-trapped region forms. Finally, we argue that the limiting case of an instantaneous black-hole-to-white-hole transition would require an unbounded violation of the null convergence condition, signalling a breakdown of the effective continuum metric description, and the need to appeal to a full quantum-gravitational description.

We investigate the constraining power of scalaron-driven inflation on asymptotically safe scalar-tensor theories. Starting from a Horndeski-type theory and applying a renormalization group improvement procedure generates higher-derivative couplings which are fixed in terms of the microscopic parameters - a structure that is expected to occur also within first principle computations based on the asymptotic safety mechanism. The latter are taken to be the free parameters appearing at the Gaussian fixed point. We find that the free parameter initially associated with the non-minimal gravity-matter coupling is not confined to the gravity-matter sector of the theory and also enters the effective higher-derivative couplings in the gravitational sector. We review the setting of multi-field inflationary models which is appropriate to analyze the inflationary dynamics in this context and illustrate their applicability by working out the explicit bounds on the non-minimal gravity-matter coupling resulting from cosmological observations. Given the fixed point structure of asymptotically safe scalar-tensor theories, the results indicate that UV-completions by two of the three available non-Gaussian fixed points can be ruled out while pinpointing phenomenologically viable RG trajectories emanating from the third fixed point.

This dissertation aims to put forth a systematic construction of a fractional-calculus extension of holographic dark energy (HDE). We show that linking late-time cosmic acceleration to non-local or memory effects encoded in a fractional (Riesz) derivative within black hole thermodynamics produces deviations from standard HDE and can address some challenges of the Hubble cutoff. In particular, a Riesz fractional spatial derivative is introduced into the Hamiltonian constraint of a Schwarzschild black hole in quantum geometrodynamics, leading to a Fractional Wheeler--DeWitt equation whose solutions yield fractionally corrected thermodynamic quantities, notably fractional Bekenstein--Hawking entropy governed by the Lévy index \(\alpha\), with \(1<\alpha\leq2\). Using this entropy with Cohen's inequality, a new dark energy density is constructed, defining the Fractional Holographic Dark Energy (FHDE) framework. The cosmological implications of FHDE are then investigated. Within the Hubble cutoff, its late-time evolution is analysed through cosmological observables, and the model is reconstructed using effective field descriptions with spin-\(0\) and spin-\(1\) candidates, allowing kinetic and potential terms to be extracted as functions of redshift \(z\) and \(\alpha\). The framework is then extended to BD, DGP, EPN, and Horndeski theories to derive the equation-of-state and deceleration parameters in terms of \(z\) and \(\alpha\). In addition, the fate of the Universe is studied through late-time singularities, namely the big, little, and pseudo-rip, within the Granda--Oliveros FHDE setting. In short, this dissertation proposes FHDE as a theoretically motivated extension of HDE, bridging non-locality in quantum gravity with the late-time dynamics of the Universe, and offering a route toward understanding cosmic acceleration beyond \(\Lambda\)CDM.

A useful warp drive must change its velocity, yet known positive-energy constructions are static or constant-velocity, while accelerating ones require exotic matter; Bobrick and Martire noted that warp drives ``do not have any natural way of changing their velocities.'' First, a conservation law settles the principle: for any asymptotically flat drive with a confined dominant-energy source and standard peeling, the Bondi--Sachs four-momentum changes only through radiation to null infinity, so the drive cannot steer without radiating. Second, we construct a positive-energy spacetime that saturates this bound. Prescribing the passenger worldtube, we take the exact Kinnersley photon rocket as exterior and solve for the matching timelike shell; the exterior and steering law are exact, while the shell is certified perturbatively and numerically. The mechanism is photon-rocket recoil on a tidally protected, exactly flat cavity; the warp drive is the decoupled flat interior, not a warp field. The exterior energy conditions reduce to $n^2\ge0$, and steering obeys $-\dot m\ge 3m|a|$, paid for by Bondi mass loss. The shell satisfies the surface dominant energy condition for $2m/R<24/25$; admissible accelerating shells exist near the Schwarzschild--Minkowski anchor and, for slow burns, as time-evolved spacetimes. A Buchdahl-type frontier $a_{\max}R\le g(2m/R)$ caps the acceleration between a numerical lower bound $\sim\!0.2$ and a closed-form ceiling ${1\over2}(1-2m/R)$. On the gravitational-wave--silent class, the optimal maneuver is the Damour dipole. The wall is marginally stable, with strict stability available at no energy-condition cost; fully dynamical flux-coupled stability remains open. The drive is causal, subluminal, and energetically costly but positive-energy: steering is a problem of energy budget, not exotic matter.

We extend the Parameterized Spin Expansion Coefficients (ParSpec) framework for ringdown tests of black holes by simultaneously sampling the characteristic length scale $\ell$ and the scaling index $p$, where the two parameters are replaced by $\tilde{p}$ and $\tilde{\ell}$ in subsequent analysis, respectively. Unlike previous analyses that fix $\tilde{p}$ to theory-motivated integer values, this extension provides a theory-agnostic description inspired by effective-field theory to the Kerr ringdown spectrum. Using \texttt{pyRing}, we apply the framework to GW250114 with informative priors on $M_{\rm f}$ and $D_{\rm L}$, comparing the $220$-only and $220+221$ mode models under different conditions on $\gamma$. The posterior distributions of $\tilde{\ell}, \tilde{p}$ and $\gamma$ are presented with different ringdown start times. We show that the posterior of $\tilde{p}$ remains largely prior dominated, indicating that current ringdown data cannot distinguish different scaling behaviors of the correction. The inferred constraint on $\tilde{\ell}$ is instead mainly controlled by the geometry of the allowed parameter space induced by the $\gamma$ condition. In particular, $\gamma<1$ provides the most natural prescription in the $(\tilde{\ell},\tilde{p})$ plane and yields stable but weak upper bounds of $\tilde{\ell}_{90}\simeq 83\, {\rm km}$. An analysis based on the Kullback-Leibler divergence further shows that, after accounting for the effective prior associated with $\gamma<1$, the data-driven information gain on $\tilde{\ell}$ and $\log\gamma$ is very small. At the current SNR level, the $220$-only model provides a more informative constraint than the $220+221$ model. We also perform a joint analysis including GW231123 and find that the combined constraint is dominated by GW250114.

We consider Bianchi IX dynamics of a Universe filled with a massless phantom field. Such an exotic matter source enables regimes impossible in vacuum or with a standard scalar field. In particular, two Kasner indices of BKL oscillations can be simultaneously negative, and the absolute value of a negative index can be large. We describe the consequences of these features and explain the nature of volume oscillations recently discovered in such a system by numerical methods.

Cross-correlation searches for gravitational-wave backgrounds depend on the geometrical configuration (physical separation and relative orientation) of the detectors comprising the network. Applying standard techniques to a few simple examples, we illustrate how the relative orientation of a pair of Earth-based L-shaped laser interferometers can drastically impact the detectability of both isotropic and anisotropic gravitational-wave backgrounds.

We investigate timelike geodesics and gravitational wave signatures of periodic motion around a static magnetically charged black hole arising from nonlinear electrodynamics and immersed in a quintessence background. We analyze the effective potential for massive particles, determine the marginally bound and innermost stable circular orbits, and classify the resulting bound trajectories using the zoom-whirl taxonomy $(\mathit{z},\mathit{w},\mathit{v})$. We show that the quintessence parameter $c_q$ systematically shifts the orbital radii, conserved quantities, and turning-point structure associated with representative periodic families. We then model the gravitational radiation emitted by periodic extreme-mass-ratio inspirals within the numerical kludge approximation. The resulting waveforms exhibit the characteristic burst-like structure of zoom-whirl motion, while variations in the quintessence coupling parameter modify the phase evolution, burst timing, and harmonic content of the signal. The corresponding Fourier spectra display a discrete comb-like structure, and the characteristic strain is concentrated in the millihertz band relevant for space-based detectors such as LISA. These results indicate that a quintessence background can leave systematic imprints on periodic orbit dynamics and on the associated time and frequency-domain gravitational wave observables.

Advances in gravitational-wave detector sensitivity have increased the rate of transient signal detections, demanding faster automated analysis. We extend MaxWave, a fast maximum likelihood wavelet reconstruction algorithm, to perform coherent multi-detector signal reconstruction and glitch rejection. We coherently search for a common set of wavelets modeling the signal in all detectors. Multi-detector data are aligned using z-statistic time and phase offsets and amplitude scalings relative to the dominant reconstruction, as well as adaptive noise weightings derived from a geometrically averaged noise spectrum. By aligning and weighting individual detectors, we form a synthetic detector that amplifies non-Gaussian features, down-weights noisy detectors, and preserves Gaussian noise statistics. We extract the coherent signal using this synthetic detector, improving sensitivity to weak events while rejecting coincident glitches that lack consistent phase and amplitude evolution. Our algorithm provides real-time, low-latency, model-independent signal reconstructions, safely denoises gravitational wave data without removing transient signals, and can complement existing burst search and reconstruction frameworks through a fundamentally distinct approach, strengthening detection confidence and improving sensitivity to diverse signal morphologies.

We investigate the polarization properties and effective stress--energy tensor of gravitational waves in metric $f(R)$ gravity within the linearized approximation around Minkowski spacetime. Owing to the additional scalar degree of freedom inherent in the theory, gravitational waves exhibit polarization states beyond the two tensor modes predicted by general relativity. Using the electric components of the linearized Riemann tensor, we derive explicit expressions for the polarization amplitudes and show that a massless scalar field excites a transverse breathing mode, whereas a massive scalar field generates both breathing and longitudinal responses through a single propagating scalar excitation. Employing the Isaacson high-frequency averaging formalism, we further derive the effective stress--energy tensor and demonstrate that both tensor and scalar perturbations contribute to the total gravitational-wave energy density. The energy transport associated with the massive scalar mode is reduced by its subluminal group velocity, leading to a frequency-dependent suppression of the scalar energy flux. These results establish a unified connection between gravitational-wave polarization and energy transport in metric $f(R)$ gravity and provide potential observational signatures for testing modified gravity with current and future gravitational-wave detectors.

The composite Quadratic Spinor Lagrangian (QSL) propagates a spin-1/2 Dirac fermion whose mass is generated geometrically by cosmological trace torsion. It is natural to ask whether promoting the spinor 1-form $\Psi_\mu$ to an \emph{independent} Dirac-vector field yields a genuine spin-3/2 dark-matter candidate. We prove that it does not. Three results combine into a no-go theorem. First, the torsional term, computed exactly by Clifford reduction, is a frame-aligned mass confined to the time-component sector -- not a uniform spin-3/2 mass. Second, the second-order form $2 D\Psi \gamma_5 D\Psi$ has identically vanishing kinetic and cross terms for the independent field: as a component expression it is the boundary part of the spinor-curvature identity and carries no bulk dynamics. Third, the genuine dynamics therefore reside in the curvature side of that identity, $S=-\int\bar\psi\psi R\sqrt{-g}$, in which the metric $g=\Psi\otimes_S\Psi$ and the scalar $\bar\psi\psi$ are \emph{both} composites of $\Psi$; the second variation consequently factors, $\delta^2S=\mathcal Q(h_{\mu\nu}[\delta\Psi],\delta\Phi[\delta\Psi])$, through the linearized metric and a scalar, both massless. Every propagating pole therefore lies on the metric light cone $k^2=0$ -- the graviton and a scalar -- and no massive spin-3/2 mode exists, on any background. This is the dynamical completion of the kinematic fact that the composite spinor 1-form has no spin-3/2 part, and it establishes the composite spin-1/2 Dirac fermion as the unique propagating matter excitation, and the unique dark-matter candidate, of the QSL. Through the super-SL(2,C) structure this surviving mode is naturally read as the Goldstino of the local supersymmetry broken by the metric condensate -- a composite, gravitational descendant of the light-gravitino dark matter of Pagels and Primack.

Generating an appreciable abundance of primordial black holes (PBHs) requires a substantial enhancement of primordial curvature perturbations on small scales. In this work, we propose a new post-inflationary mechanism in which such an enhancement arises during a stiff, or kination, epoch. The mechanism is driven by metric vector perturbations sourced by the vector component of the electromagnetic stress-energy tensor associated with primordial magnetic fields (PMFs). Since these first-order vector modes remain approximately constant during kination, they act as persistent nonlinear sources for second-order scalar perturbations. We show that the resulting vector-induced curvature perturbations are amplified toward the infrared cutoff of the kination band and exhibit the characteristic scaling $\mathcal P_{\mathcal R}(k)\propto k^{-5}$. As a concrete realization, we consider PMFs generated in a Ratra-type magnetogenesis scenario and find that the induced curvature perturbations can produce PBHs with an abundance large enough to constitute a substantial fraction of the dark matter.

We study the production of spin-$1/2$ particle-antiparticle pairs in curved spacetimes with nontrivial dependence on more than one coordinate. To this end, we develop two complementary approaches. First, we extend the scattered-wave-function (SWF) method, originally introduced for pair production in electromagnetic backgrounds, to curved spacetime backgrounds. Second, we complete the development of an open-worldline-instanton method by deriving the pre-exponential factor of the pair-production probability. We apply both methods to several two-dimensional metrics and find good agreement between the resulting probabilities. While the SWF approach provides numerically exact results and is particularly efficient for the examples considered here, the instanton approach offers favorable scaling to higher-dimensional backgrounds and more extreme parameter regimes. These methods provide new tools for studying pair production in multidimensional gravitational backgrounds beyond the reach of many existing approaches.

In gravitational wave detectors, optical aberrations arise mainly from laser absorption in coatings and production process defects in the optics along the laser path. If left uncorrected, these optical path distortions drive the interferometer away from its optimal working point, degrading both stability and sensitivity. Future instruments such as the Einstein Telescope high-frequency detector will operate with unprecedented circulating power, further amplifying the aberration budget. In the current detectors Advanced Virgo and Advanced LIGO, the axisymmetric distortions are corrected using thermal actuators and CO2 laser projectors, however, non-axisymmetric wavefront distortions remain unmitigated. Deformable mirrors are investigated as a flexible solution for mitigating such defects: by shaping the CO2 beam phase upon reflection, they can imprint the required asymmetric intensity pattern on the lensing optics without introducing frequency dependent noise. The target phase map is computed via a modified Gerchberg-Saxton algorithm. We present simulations of this projection strategy and experimental validation demonstrating consistent reproduction of the desired intensity patterns.

The gravitational production of dark matter from stochastic gravitational waves requires the produced fermion to acquire a mass by unspecified late-time physics. We show that this mass is supplied by spacetime torsion alone -- no Higgs sector and no free mass parameter. In the Quadratic Spinor Lagrangian formulation of general relativity, extended to Einstein--Cartan, a cosmological spinor condensate generates a vectorial trace torsion $K\propto\dot\chi/\chi$; an explicit Clifford reduction confers on the produced spin-1/2 fermion a pure Dirac mass $M_{\rm eff}=(1/\sqrt6)\,|\dot\chi/\chi|$, with no pseudoscalar or cross terms, locked to the Hubble rate at production, $M_{\rm eff}\simeq(c_\chi/\sqrt6)H_*$. The relic abundance is then a one-parameter prediction, $\Omega h^2\propto H_*^{5/2}$, and the spin is fixed: the same framework admits no propagating spin-3/2 mode, so the composite spin-1/2 Dirac fermion is its unique dark-matter candidate.

We study future-pointing timelike solutions of the Lorentz force equation in the sub-extremal Kerr--Newman spacetime, with special attention to the time-machine region $\mathfrak T$, where the axial Killing field $\partial_\phi$ is timelike. We first construct smooth closed electromagnetic orbits tangent to $\partial_\phi$ in the positive equatorial part of $\mathfrak T$: the radius of such a circle determines, and is determined by, the charge-to-mass ratio of the particle which must have opposite sign to that of the black hole charge. We then prove the existence of spherical electromagnetic orbits contained in the equatorial time-machine region and derive explicit relations between their radius, charge-to-mass ratio, energy and angular momentum. Next we give sufficient conditions ensuring that an equatorial electromagnetic orbit is a flyby orbit with radial turning point in $\mathfrak T$. Finally, to describe charged-particle decay processes whose fragments have different charge-to-mass ratios, we introduce the notion of a broken electromagnetic orbit: a continuous, piecewise smooth, future-pointing worldline whose smooth pieces solve the Lorentz force equation. Imposing conservation of kinetic four-momentum and electric charge at the decay vertices, we exhibit an energy extraction process followed by a causality-violating one. The latter is realized by a closed broken electromagnetic orbit, which we construct in both the $r$-positive and the $r$-negative regions inside the inner horizon, by concatenating two flyby branches sharing a common radial turning value $\bar r$, and having charge-to-mass ratios with opposite sign to that of the black hole charge, with a spherical electromagnetic orbit of radius $\bar r$.

The gravitational-wave induced freeze-in of Maleknejad and Kopp (2026) produces dark fermions from a stochastic gravitational-wave background, but requires them to acquire mass by separate means. We develop the Quadratic Spinor Lagrangian (QSL) formulation of general relativity, extended to Einstein--Cartan, as a framework that supplies this mass geometrically. The spinor 1-form built from a single Dirac field is purely spin-1/2 -- its gamma-traceless (spin-3/2) part vanishes identically -- so the propagating excitation is a Dirac fermion, the same content as the produced Weyl fermion. A cosmological spinor condensate sources a vectorial trace torsion $K\propto\dot\chi/\chi$, and an explicit Clifford reduction shows that this torsion gives the fermion a pure Dirac mass $M_{eff}=(1/\sqrt6)\,|\dot\chi/\chi|$, with no pseudoscalar or cross terms. The mass is not a free parameter but is locked to the Hubble rate at production, $M_{eff}\simeq(c_\chi/\sqrt6)H_*$, making the relic abundance a function of essentially the single scale $H_*$ ($\Omega h^2\propto H_*^{5/2}$) and supplying the mass the parent mechanism must postulate. Whether promoting the spinor 1-form to an independent field yields a propagating spin-3/2 candidate is a distinct dynamical question; Paper II shows that it does not -- the QSL channels all propagation into the gravitational sector -- so the composite spin-1/2 Dirac fermion is the unique QSL dark-matter candidate. We discuss the resulting dark-matter phenomenology and its link to asymptotically free scalar-field cosmology.

We study the quantum dynamics of the dynamical region of the Reissner--Nordström geometry using a minisuperspace reduction and affine quantization, which is naturally suited for positive-definite geometrical variables. The resulting Wheeler--DeWitt equation becomes separable, yielding Hermite-polynomial modes in one sector and Gaussian-like radial solutions in the other. Affine quantization introduces additional short-distance contributions that modify the small-radius behaviour of the wave function. By constructing normalizable semiclassical wave packets, we analyze the resulting probability distributions in minisuperspace and the role played by the electric charge in the quantum dynamics. Our results extend previous affine-quantization studies of the Schwarzschild case to the charged Reissner--Nordström geometry.

We investigate test particle dynamics and gravitational wave (GW) phenomenology in an exact spherically symmetric vacuum solution of Freund - Nambu scalar - tensor gravity. This framework generalizes the Janis - Newman - Winicour (JNW) naked singularity via a geometric non - linear coupling $q$ and a direct scalar - particle coupling $g_s$. We demonstrate that these parameters systematically modify the Innermost Stable Circular Orbit (ISCO) - which shifts inward for $g_s > 0$ - and the Marginally Bound Orbit (MBO). Furthermore, we classify bound periodic trajectories to isolate extreme zoom - whirl orbits exhibiting intense periapsis precession. By applying the Numerical Kludge method to Extreme Mass - Ratio Inspirals (EMRIs), we reveal that scalar - tensor corrections induce a macroscopic temporal dephasing in high - frequency GW bursts, even when the orbit's spatial topology is preserved. These unique phase shifts offer a robust diagnostic signature for future space-based observatories like LISA to probe the strong - field regime and constrain scalar - tensor extensions of general relativity.

We perform 3D hydrodynamics simulations of an equal-mass quasi-circular live $10^6~{\rm M}_\odot$ massive black hole binary (MBHB) embedded in a prograde, locally isothermal circumbinary disk (CBD) with $0.1$ aspect ratio. The binary evolution is driven by the gaseous torques and its dynamics is described with $2.5$ post-Newtonian corrections. This approach allows us to track the influence of the CBD on a gravitational-wave (GW) driven MBHB inspiral from $55$ to $46$ Schwarzschild radii, i.e., at its early evolution in the LISA band at redshift $z\sim1$. For the first time for the $0.1$ aspect ratio disk, we report the measurement of gravitational and accretion torques with and without concurrent GW emission. We also report how the morphology of the accretion time series onto the MBHB modestly alters when GW emission is the dominant binary evolutionary mechanism. Lastly, we find that the gas-induced orbital phase-shift is $0.12$ rad over $600$ orbital cycles, which LISA should detect at $z=1$. Our results have implications for multi-messenger astronomy, since observation of accretion rate modulation by LSST/Roman surveys and phase-shift by LISA will provide crucial information on the complex environment surrounding MBHBs.

Since the Fermi satellite's identification of a candidate $\gamma$-ray burst (GRB) temporally coincident with GW150914, several tentative, and often debated, associations between electromagnetic (EM) transients and gravitational-wave (GW) signals from binary black hole (BBH) mergers have been reported. One such event, S241125n (later confirmed as GW241125_010116), was identified during the fourth observing run (O4) of Advanced LIGO and found to be spatially (within large GW localization uncertainty) and temporally coincident with a subthreshold GRB detected by the Swift Burst Alert Telescope Gamma-ray Urgent Archiver for Novel Opportunities (BAT-GUANO). Here, we present results from a radio follow-up campaign targeting the BAT-GUANO localization region, carried out with the Karl G. Jansky Very Large Array (VLA). We also re-analyze Swift/XRT observations of the field, and combine these results with optical upper limits. Our analysis constrains the isotropic kinetic energy of a putative relativistic jet launched in the BBH merger to $\lesssim 3 \times 10^{50}$ erg for $n_{ISM} = 1.0 cm^{-3}$. We also discuss both the challenges and the diagnostic power of radio follow up in assessing candidate BBH-GRB associations, and present projections for analogous radio studies in the LIGO-Virgo-KAGRA observing run 5 (O5), and in the era of next-generation ground-based instrumentation. The enhanced sensitivity and localization capabilities of detector networks such as Cosmic Explorer and the Einstein Telescope, paired with the enhanced sensitivity of next-generation radio interferometers such as the next-generation VLA and the Square Kilometre Array, will significantly strengthen coordinated multi-messenger follow-up of BBHs. These next-generation facilities are likely to provide an answer to whether BBHs host relativistic ejecta powered by mini-disk accretion.

The renormalization of the primordial inflationary power spectrum has long raised the possibility that ultraviolet effects could significantly alter predictions for cosmological observables. We demonstrate that inflation dynamically suppresses the entire renormalization sector: while super-Hubble perturbations freeze after horizon crossing, renormalization contributions decay rapidly during inflation. As a consequence, the observable primordial spectrum is remarkably insensitive to renormalization ambiguities, providing strong evidence for the robustness under renormalization of standard inflationary predictions at observable scales.

The dark bubble model explains the existence of a positive cosmological constant by making explicit use of the instabilities underlying the de Sitter swampland conjectures to make the accelerated expansion of the universe inevitable. A distinctive consequence of the construction is a unique hierarchy connecting cosmological, gravitational, string, and higher-dimensional scales. In particular, the model naturally predicts the existence of a dark dimension of micron size, an idea that has been argued for on independent grounds in the literature. The same framework also predicts a weakening of gravity at distances of order the dark-dimension scale, leading to a fading of the gravitational force at micron distances. We argue that the dark bubble therefore provides a concrete realization of both the dark dimension proposal and Sundrum's fat graviton scenario, in which gravity effectively ceases to probe shorter distances. Additional predictions include a string scale of order tens of TeV and a measurable positive spatial curvature of the universe. We review these key aspects of the model, discuss their implications for gravity and cosmology, and highlight its key predictions.

The rapid appearance of supermassive black holes at high redshift motivates a reassessment of non-baryonic growth channels. We develop a loss-cone framework for collisionless dark-matter (DM) capture by early black-hole seeds, with particular attention to phase-space depletion and refilling. The calculation combines Eddington-inverted NFW-like halos, a relativistic direct-capture boundary, and an orbit-averaged Fokker-Planck treatment of angular-momentum transport. Primordial black holes (PBHs) are treated as massive perturbers whose refilling strength depends on both their abundance and individual mass. Collisionless refilling by triaxial or chaotic centrophilic orbits is included as a phenomenological upper-envelope channel. We show that ordinary stellar relaxation gives negligible DM-driven growth for the fiducial high-redshift seeds. PBH-driven granularity can yield order-of-magnitude growth in sufficiently compact halos, while triaxial or full-loss-cone supply can produce a rapid early burst. In the self-consistent calculations, however, the evolution generally becomes supply-limited. Once the accessible low-angular-momentum phase-space reservoir is depleted, the capture rate collapses and the black-hole mass saturates. Fixed-background NFW calculations therefore overestimate sustained growth, especially in the full-loss-cone limit. A TNG50-calibrated NFW benchmark gives negligible growth even under optimistic refilling assumptions. Collisionless DM capture is therefore unlikely to solve early SMBH growth in generic NFW-like halos, but it can provide a radiatively dark upper envelope in rare compact environments with efficient angular-momentum refilling.

The holographic time-like entanglement entropy (TEE) extends entanglement to time-like boundary subregions. While its definitive holographic dictionary remains debated, one concrete proposal utilizes piece-wise extremal surfaces. In this work, we adopt this geometric prescription as an exploratory framework to holographically investigate the late-time ($\tau_0\to \infty$) growth of TEE in asymptotically AdS black holes with a space-like singularity and no inner horizon. By assuming a Kasner geometry near the space-like singularity and using null energy condition, we analytically show that a critical extremal surface $\mathcal{A}_c$ inside the event horizon completely governs the late-time linear growth of the TEE. This result suggests that the late-time behavior of TEE is tightly constrained by the geometry of black hole interiors. Using numerical results from Einstein-scalar theory, we find a robust behavior: the vacuum Schwarzschild-AdS geometry sets an upper bound on the growth rate of the real part and a lower bound on the imaginary part. We prove these bounds in static planar symmetric case under dominant energy condition and conjecture that it should be true in more general cases.

Newtonian noise is expected to be the dominating noise source for low frequencies at the Einstein Telescope. It originates from seismic waves that cause density fluctuations in the rock around the interferometer. The mitigation strategy for Newtonian noise relies on an array of seismometers, placed at depth in boreholes, which provides measurements of the seismic wave field. We optimize the positions of the individual seismometers for the mitigation capabilities of the array for a full corner of the Einstein Telescope. We find that the mitigation capabilities of arrays with multiple seismometers in each borehole match the capabilities of only somewhat smaller arrays but with only one seismometer per borehole. Mitigation is further improved by extending the array with seismometers in the interferometer tunnels. Such configurations may hence provide a cost-effective way towards realizing an efficient seismic array. In each case, we quantify the broadband mitigation performance in the range from 1 to 10 Hz for arrays that are optimized for a frequency of 10 Hz, as well as the robustness of the arrays with respect to variations from their optimized positions. We find that larger arrays with several seismometers per borehole and additional seismometers in the tunnels provide promising broadband performance above 3 to 4 Hz and that such arrays are particularly stable against variations in the seismometer positions with mitigation factors $>6$ for an array of 20 boreholes with 3 seismometers each and $>15$ for a large array of 50 boreholes with 10 seismometers.

The dimensionless tidal deformability, $\Lambda$, of neutron stars (NSs), inferred from gravitational-wave (GW) observations, has thus far been used primarily to constrain the pressure of dense matter near twice nuclear saturation density, leaving the core equation of state (EOS) largely inaccessible to inspiral-phase GW observations. We show that the core EOS can be probed directly through $\Lambda$ using a perturbative analysis of the dimensionless stellar-structure and tidal-response equations formulated in terms of scaled intrinsic variables, without invoking any specific EOS model. We uncover a remarkable EOS-insensitive scaling relation between $\Lambda$ and the central EOS parameter $\mathrm{X}\equiv P_{\rm c}/\varepsilon_{\rm c}$, where $P_{\rm c}$ and $\varepsilon_{\rm c}$ denote the central pressure and energy density, respectively. The relation is validated against a broad ensemble of physically viable EOSs. Applying it to tidal deformabilities inferred from events such as GW170817 enables a direct determination of $\mathrm{X}$. We further derive a tight lower bound, $\Lambda_{\rm{TOV}}\gtrsim 9.2^{+1.2}_{-1.2}$, for maximum-mass NSs along stable mass-radius sequences, quantitatively demonstrating that even the most compact stable NSs remain distinctly separated from black holes, for which $\Lambda_{\rm{BH}}=0$. These findings reveal a previously unrecognized connection between inspiral-phase tidal deformability and the core EOS, establishing a direct link between GW observables and the microphysics of ultradense matter in the strong-gravity regime. The resulting scaling establishes inspiral-phase tidal deformability as a direct and largely model-insensitive probe of the EOS of NS cores.

We consider the classification of toric self-dual Einstein gravitational instantons with negative cosmological constant. As is well known, any Killing vector field on a self-dual Einstein manifold defines a local conformal Kähler structure. We prove that if the conformal Kähler structure associated to one of the torus Killing fields is global and extends to an ALE manifold with no additional fixed points, then the corresponding self-dual Einstein instanton is precisely given by the infinite class of multipole solutions constructed by Calderbank, Pedersen and Singer.

Wave-optics interference in strongly lensed gravitational waves is a new interferometric probe of dark matter substructure: a subhalo population threading a galaxy-scale lens imprints frequency-dependent distortions on the amplification factor of each macro image. In a companion paper (arXiv:2603.04267), we computed these imprints for the magnified minimum image. Here, we extend the calculation to the saddle-point image and we assess the detectability of the combined signal with the Laser Interferometer Space Antenna (LISA). Evaluating the amplification factor at a saddle is numerically delicate, because the equal-arrival-time contours are open and the subhalo signal is a small difference of large terms; we present a time-domain method that resolves it. Across a Monte Carlo ensemble of cold dark matter subhalo realizations, subhalos induce percent-level amplitude and phase modulations in both image parities, while the mean (de)magnification splits by parity: the minimum is net magnified and the saddle net demagnified. Demodulating the macro-image interference recovers the per-image modulations, and a matched-filter analysis that projects out the lens parameters yields a combined detection above $5\sigma$ in $62\%$ of realizations for fiducial massive-black-hole-binary sources of total mass $\sim10^{6}\,M_\odot$ at redshift $1.5$, provided the source lies close to the lens caustic at small impact parameter $y_{\rm src}\lesssim0.1$. Folding these naive per-event significances through optimistic strong-lensing rate forecasts yields $10$-$20$ substructure detections over the LISA mission. Strongly lensed gravitational waves are thus a sensitive, complementary probe of substructure at $10^{4}$-$10^{7}\,M_\odot$ scales inaccessible to electromagnetic observations.

Asymptotically safe quantum gravity is an approach to quantum gravity. It is based on the premise that quantum field theory can describe the quantum nature of gravity in our universe. At its core lies quantum scale symmetry. This review provides an introduction to the key ideas of the approach and surveys the current status of the field. Over the last years, the field has taken large strides towards an increasingly realistic setting: First, compelling evidence for quantum scale symmetry exists in four-dimensional, Euclidean, pure gravity, establishing the Reuter fixed point robustly. Second, matter fields, including the Standard Model as well as beyond-Standard-Model-candidates, have been studied in depth, with increasingly conclusive evidence for quantum scale symmetry. Most recently, the final gap to a realistic description of quantum gravity is being closed, because Lorentzian spacetime signature can now be accounted for. As a consequence of quantum scale symmetry in the ultraviolet, the approach is highly predictive at all scales. This review discusses the physics of asymptotic safety across all scales. Predictive power for particle physics, black holes and cosmology provides a clear pathway to confronting quantum gravity with current and near-future observations. The review closes by discussing the connection to other approaches to quantum gravity. It advocates the perspective that such connections between approaches may lead us to an understanding of universal physical features of quantum gravity.

If one extends the AdS/CFT extrapolate dictionary to large but finite $N$, we are expected to obtain non-perturbative violations of bulk micro-causality. Previously this was achieved by implementing a late boundary time cut-off, while smearing the boundary operator via the HKLL kernel. By performing explicit bulk reconstructions in the backgrounds of near-horizon modified AdS$_2$ and BTZ black holes, we recover the same non-locality estimates as above. For these black hole mimickers, the near-horizon modification is controlled by a throat parameter which sets the scale of this non-locality. In three bulk dimensions, probe dynamics also exhibits a dip-ramp-plateau structure in their spectral form factor when averaged over the throat parameter. Such structure has also been found recently in the background with a stretched horizon or a brick wall.

Resolving the impact of magnetic field instabilities in triggering small scale turbulent flow and the associated rearrangement of the field is of critical importance in understanding multimessenger observables in binary neutron star mergers, and angular momentum transport in neutron stars and accretion disks. Direct simulation of these instabilities are unfeasible, however large-eddy simulations can incorporate the impact of this turbulence with a subgrid model. We present the first machine-learning-based subgrid model for special relativistic magnetohydrodynamics, trained using a neural network. We demonstrate its performance in online simulations of the 3D Kelvin-Helmholtz instability through both a priori and a posteriori tests. Evaluated in a low resolution simulation, our model captures magnetic field amplification of a simulation at 4 times the resolution with a speed-up of a factor 44. This demonstrates the applicability of such methods in general relativistic simulations of neutron star mergers and other scenarios.

Recent baryon acoustic oscillation measurements from DESI provide important new clues for reassessing whether the standard $\Lambda$CDM model offers a sufficient description of the late-time expansion history of the Universe. When combined with cosmic microwave background and type Ia supernova data, these measurements show an apparent departure from the $\Lambda$CDM model, commonly described as dynamical dark energy (DDE) with equation of state crossing the phantom divide (i.e., quintom behavior). This review examines the current status of the DESI-motivated indications for DDE and their possible implications for physics beyond $\Lambda$CDM. We discuss how the strength of the preference for DDE depends on the adopted parametrization and dataset combination, and how residual systematics or internal tensions among datasets may affect its interpretation. At the background level, several mechanisms beyond $\Lambda$CDM can produce similar expansion histories. We therefore further discuss how the same effective departure from $w=-1$ may arise from physically distinct scenarios, including interacting dark energy, non-minimally coupled gravity, and non-standard dark matter. Meanwhile, these different new-physics interpretations may have different implications for current cosmological tensions, especially those involving $H_0$, $S_8$, and $\sum m_\nu$. In conclusion, the question posed by DESI is not merely whether dark energy evolves with time, but rather how, within the framework of precision cosmology, to disentangle new physics scenarios from systematic errors.

The families of Lorentzian distance functions to and from points along a complete timelike line in a spacetime are known to be locally equi-Lipschitz continuous in a neighborhood of the line. This is an essential component in the proof of the classical Lorentzian splitting theorems. We show that this property fails in general for families of Lorentzian distances to and from the level sets of a given Cauchy temporal function. Moreover, we formulate conjectures based on the existence of Cauchy temporal functions in cosmological and timelike geodesically complete spacetimes such that the Lorentz distances to its level sets are equi-Lipschitz, which are equivalent to Bartnik's splitting conjecture.

We investigate a quintessence dark-energy model with an exponential potential and an exponential coupling to cold dark matter (CDM), hereafter referred to as the CQ-EXP model, using Planck CMB, DESI BAO, and DES-Dovekie supernova observations. We also examine how variations in the neutrino mass sector affect the constraints. When the neutrino mass sum is fixed at $\sum m_\nu=0.06$ eV, the data favor a coupling between quintessence and CDM, with the coupling parameter $\beta$ deviating from zero at more than $3\sigma$. In particular, the observations favor the $\beta<0$ branch, where the energy transfer between the two dark sectors changes sign and the effective equation of state (EoS) of dark energy crosses the phantom divide, $w=-1$. When the effective neutrino mass parameter $\sum m_{\nu,\mathrm{eff}}$ is treated as a free parameter, the data show a preference for negative values of $\sum m_{\nu,\mathrm{eff}}$. This additional freedom weakens the preference for the coupling between quintessence and CDM and leads to nearly identical values of $\chi^2_{\rm min}$ for the CQ-EXP models with $\beta>0$ and $\beta<0$, corresponding respectively to models without and with phantom-divide crossing in the effective EoS. Both values are slightly larger than that obtained in the $w_0w_a$CDM model, indicating that the CQ-EXP model cannot be statistically distinguished from the $w_0w_a$CDM model with the data considered here. Therefore, when $\sum m_\nu$ is fixed, current observations favor the CQ-EXP model with phantom-divide crossing. In contrast, when negative values of $\sum m_{\nu,\mathrm{eff}}$ are allowed, a CQ-EXP dark energy without crossing $w=-1$ can also provide an effective explanation of the latest observations.

We investigate a discrete warped Chern-Simons description of three-dimensional warped gravity based on boundary holonomies and monodromy sectors. Starting from the lower-spin SL(2, R) + U(1) gauge structure associated with warped AdS(3) holography and warped conformal field theories (WCFTs), we construct a discrete boundary framework in which ordered products of link holonomies replace continuous gauge connections along noncontractible cycles. In this setting, boundary monodromies become the primary gauge-invariant observables characterizing the physical sectors of the theory. We show that the hyperbolic, eliliptic, and parabolic sectors naturally arise from the conjugacy classes of the discrete SL(2, R) monodromy, while the additional U(1) holonomy supplies the warped contribution to the boundary charges. Using these monodromy invariants, we derive a discrete entropy relation entirely from boundary holonomy data without relying on a smooth geometric thermal background. The resulting entropy reproduces the characteristic warped black-hole and WCFT structure in the continuum limit. We further demonstrate that the continuum warped holonomy conditions are recovered from the large-lattice limit of the ordered boundary products, establishing a direct correspondence between discrete monodromies and continuous Wilson loops. Our analysis suggests that warped gravitational thermodynamics may be understood from a fundamentally holonomy-based perspective in which boundary monodromy sectors provide an alternative organizational description of the physical states within the discrete warped framework. Keywords: warped Chern-Simons theory, boundary monodromies, holonomy sectors, Wilson loops, warped thermodynamics.

We formulate an operator-algebraic mechanism by which exact Boolean records can arise from local completely positive quantum operations without being imposed as microscopic structure. The kinematic input is an algebraic process functional assigning probabilities to local normal completely positive operations in a finite operational context. From the predual response of a target algebra to source interventions, relative to a background strategy class, we define an influence algebra; exact events are then, by definition, the projections in its center. The dynamical question is whether nontrivial centers can be generated by coarse-graining rather than inserted through split-record laboratories. We address this question using state-preserving normal unital completely positive coarse-graining channels. If the Cesaro means of such a channel converge to a Choi-Effros infrared range and the range is asymptotically abelian in the GNS seminorm, then the represented infrared algebra is a commutative von Neumann algebra. Its projection lattice is therefore a complete Boolean algebra. We also give a finite-sector block-primitive criterion, motivated by locality and scrambling, which implies this asymptotic abelianness with exponential suppression of off-sector coherences and intra-sector fluctuations. The result is a conservative mathematical statement: classical facts are not identified with arbitrary projections of a Type-III local algebra, but with central projections selected by an asymptotically abelian completely positive infrared limit.

Warm inflation is usually expected to completely deplete the inflaton condensate by dissipating its energy into radiation. We show that this expectation fails in a simple and observationally viable regime. In a strongly dissipative warm inflationary scenario, the dissipative ratio, $Q=\Upsilon/(3H)$, can fall rapidly after the end of inflation as the system approaches radiation domination, thereby suppressing further energy transfer to the thermal bath. This leads to a residual inflaton condensate, which subsequently evolves as an effectively non-dissipative scalar field. For potentials with a stable quadratic minimum, this remnant inflaton manifests as a cold dark matter component. We establish this mechanism for the minimal renormalizable potential, with a dissipative coefficient $\Upsilon\propto T^3$. In this case, current cosmological data allow strong dissipation while leaving the inflaton mass weakly constrained by inflationary observables. The observed dark matter abundance then fixes its mass to be $m \approx 0.02\,{\rm MeV}$, while larger masses overclose the Universe. The transition to matter-like scaling occurs well before BBN, avoiding a long-lived inflaton dark radiation component. Relic inflaton dark matter therefore turns the post-inflationary dynamics of warm inflation into a new late time constraint on its parameter space.

We present a novel method to conduct targeted gravitational-wave searches for compact binary mergers using the GstLAL inspiral pipeline. By incorporating sky localization and timing information from external electromagnetic triggers, we enhance the sensitivity of the search for sub-threshold gravitational-wave signals associated with events such as short gamma-ray bursts. Our approach modifies the standard likelihood ratio ranking statistic to include a sky localization prior, allowing for a more focused analysis on specific regions of the sky. We demonstrate the effectiveness of this method through injection studies, comparing the performance of the targeted search against the standard all-sky search configuration. The results show a significant improvement in detection efficiency for signals consistent with the provided sky location and timing, while maintaining control over false alarm rates. This targeted search framework enables rapid follow-up of electromagnetic transients, facilitating multi-messenger astronomy efforts in the era of advanced gravitational-wave detectors.

In this study, we numerically investigate Bondi-Hoyle-Lyttleton (BHL) accretion around Kerr-Sen black holes and examine how the charge-related deformation of the spacetime affects the shock-cone morphology, the variation of the mass accretion rate, and the quasi-periodic oscillation (QPO)-like temporal behavior. The relativistic BHL flow is solved numerically in the equatorial plane for two different black hole spin parameters, a = 0.9 M and a = 0.5 M. From the numerically computed mass accretion rate signal, we calculate the power spectral density (PSD) and perform multi-component Lorentzian fits to identify the dominant QPO-like modes excited around the black hole. The results show that the Kerr-Sen deformation shifts the characteristic frequencies, changes the coherence properties of the oscillation modes, and produces near-resonant harmonic structures close to 3:2 and 2:1. By using inverse mass scaling, the numerically computed frequencies are compared with observed QPOs from stellar-mass, intermediate-mass, and supermassive black hole systems. In particular, reasonable agreement between the numerical simulation results and observations is found for the sources GRS 1915+105, IGR J17091-3624, M82 X-1, NGC 5408 X-1, RE J1034+396, 1H 0707-495, and ESO 113-G010. This comparative analysis indicates that Kerr-Sen black hole shock-cone oscillations may provide a unified framework for interpreting timing features over a broad range of black hole masses and may additionally contribute to constraining the mass and spin parameters of sources whose properties are not yet fully established observationally. These findings further imply that combined hydrodynamical and timing diagnostics constitute a promising approach for assessing the extent to which deviations associated with the Kerr-Sen geometry can be empirically distinguished from those of the Kerr spacetime.

Witten's conformal boundary condition \cite{Witten:2018lgb} provides an elliptic boundary-value problem for the finite-boundary perturbative Euclidean gravitational path integral: one fixes the boundary conformal class and the mean curvature, while the trace-free extrinsic curvature is left free as the conjugate response. We show that this perturbative construction admits no half-supersymmetric extension in linearized minimal supergravity. For fixed conformal bosonic data, no half-dimensional gravitino boundary condition (local or pseudodifferential, APS-type included, with any compatible ghost condition at highest-derivative order) closes the full preserved chiral supersymmetry. Supersymmetry first selects the natural local chiral gravitino datum. Acting back on this datum then produces the trace-free extrinsic curvature, precisely the response that the conformal prescription leaves unfixed. The obstruction is therefore not the failure of a particular elliptic ansatz: even the chiral/Robin completion that is LS-elliptic and BRST-compatible at highest-derivative order would impose Dirichlet control on a Neumann response. The obstruction is pointwise in tangential momentum and survives compensating gauge transformations. It is a linearized, highest-derivative obstruction, not a global or nonlinear no-go; nonlinear supercovariant boundary terms may evade it by tying the trace-free extrinsic curvature to gravitino bilinears.

An outstanding problem in the framework of conformal thermodynamics concerns the interpretation of variations in the central charge $C$. In this paper, we construct a novel central-charge Rényi entropy via the Casini-Huerta-Myers (CHM) map by considering thermal CFTs on a hyperbolic cylinder within a fixed charge, field theory volume and central charge potential $(\tilde{Q},\mathcal{V},\mu_C)$ grand canonical ensemble. We demonstrate that the resulting entropy satisfies all four fundamental Rényi entropy inequalities throughout the admissible range of $\mu_C$, establishing its consistency as a genuine Rényi measure. Physically, this novel measure extends conventional Rényi entropy by capturing the degree of entanglement across a statistical ensemble of holographic CFTs with fluctuating degrees of freedom. Furthermore, our conformal thermodynamic analysis of near-extremal configurations reveals that residual entropy arises from the central charge sector rather than thermal excitations. The mass gap that separates the extremal state and the first thermal excitation introduces a characteristic temperature scale $\tilde{T}_*$, which translates via the CHM map into a distinguished characteristic Rényi index $n_*$. Crucially, we propose that $n_*$ separates the theory space into two qualitatively distinct statistical regimes: a dominant-theory regime ($n > n_*$) governed by the most probable CFT realizations, and a multi-theory regime ($n < n_*$) where a broader spectrum of fluctuating theories and higher-energy modular excitations becomes increasingly relevant.

In our recent paper arXiv:2509.00552, we used a stringy model for quantum space-time foam to suggest that the so-induced subluminal Lorentz violation~(LV) for photons would not lead to experimentally unacceptable changes in the developments of particle showers initiated by cosmic $\gamma$-rays in the Earth's atmosphere, in contrast to other approaches to LV. The result indicated, nonetheless, at the same time that the foam can mildly modify the electromagnetic cascades under certain conditions, by suppressing pair creation on nuclei by primary photons. In this addendum, we consider how this modification affects the detection of extensive air shower~(EAS) initiated by an ultrahigh-energy cosmic-ray particle~(viz., a primary hadron), like proton with $E \sim 10^{19}~\textrm{eV}$, given that secondary photon subshowers following $\pi^{0}$ decays could be similarly influenced. We argue that fewer electrons would reach the detector and hence the energy of the primary particle may be underestimated due to foam effects, enhancing in such a way the muon content in EASs. This opens up the possibility of interpreting the alleged ``excess'' of muons, as reported by Auger and Telescope Array collaborations recently and many other experiments on high-energy cosmic rays, with a quantum-gravitational effect. Future observations are anticipated to confirm whether this anomaly really exists.

The Laser Interferometer Space Antenna (LISA) is a space-based gravitational-wave observatory that uses free-falling test masses as inertial references to detect milliHertz frequency signals. Interactions between test masses and galactic or solar energetic particles cause charge buildup and Coulomb forces, source of acceleration noise that must be accurately modeled. LISA Pathfinder measurements showed that the Poissonian test mass charging noise was considerably larger than that in pre launch simulations, indicating missing physical processes in early models. Emission of low energy secondary electrons (LEE) from test mass and housing surfaces has been proposed as a key mechanism affecting charging and the sensor electrostatic response. We report a particle accelerator based experiment that directly tests the LEE hypothesis by measuring proton induced test mass charging in a LISA like Gravitational Reference Sensor geometry as a function of the test mass electrostatic potential.

We compute the next-to-leading order (NLO) angular impulse (spin kick) in the scattering of Kerr black holes using the Kosower--Maybee--O'Connell (KMOC) formalism. Our approach is based on on-shell scattering amplitudes and leading singularities, allowing for a direct extraction of classical observables from quantum amplitudes. We derive compact expressions for the spin-dependent angular impulse valid to all orders in the spin variables at the integrand level, and show that these results reduce to known expressions in the appropriate limits. We perform detailed consistency checks: the conservative result preserves both the covariant spin supplementary condition and the spin magnitude through 2PM order, and the quadratic-in-spin conservative result agrees with existing radial-action results after translating between the direct KMOC spin kick and the radial-action observable. In addition, we extract the corresponding non-relativistic gravitational potential from the triangle leading singularities, obtaining a representation that resums spin effects and reproduces the known spin-orbit interaction at linear order. Our results provide further evidence for the efficiency of amplitude-based methods in classical gravitational dynamics, and highlight the KMOC formalism as a powerful framework for computing spin-dependent observables in binary black hole scattering.

The dynamics of a massive scalar field non-minimally coupled to gravity in an expanding de Sitter universe are investigated. It is shown that a comoving observer identifies the Bunch--Davies state as the vacuum, whereas a static observer perceives the same state as a thermal bath at the Gibbons--Hawking temperature. Motivated by this observer dependence, a thermal formulation based on Thermo Field Dynamics is developed by combining the geometric doubling associated with the cosmological horizon with the statistical doubling induced by a intrinsec thermal bath. The resulting construction reveals that the doubling procedure is not merely a mathematical artifact, but rather a manifestation of the global causal structure of spacetime together with finite-temperature effects. The temporal evolution of the Bogoliubov angle is analyzed and the corresponding particle number densities are evaluated in both comoving and static frames. In the radiation limit, the comoving number density remains conserved, providing a thermodynamic evolution consistent with that of the Cosmic Microwave Background, whereas in the static frame finite-temperature effects sti\-mulate Parker particle creation. For massive and non-minimally coupled fields, the interplay between geometric and statistical temperatures gives rise to a characteristic thermal scale and a nontrivial dependence on the initial conditions. These results provide a unified framework for describing quantum fields in de Sitter spacetime in the presence of both apparent horizon-induced and intrinsec thermal effects.

Warm inflation perturbations are sourced by both thermal and quantum fluctuations and are commonly computed through stochastic realizations of the perturbation equations, as implemented in the publicly available code SWIM. Deterministic formulations based on correlation matrix evolution provide a computationally efficient alternative, but can become numerically ill-conditioned when the perturbation variables evolve over widely different scales. In this work, we extend SWIM by introducing a deterministic module, DSWIM, based on correlation matrix evolution. We introduce a physically motivated scaling matrix transformation derived from the effective Hubble scaling of the perturbation variables. The transformed system preserves the primordial curvature power spectrum exactly while substantially improving the numerical conditioning of the deterministic evolution equations. Using representative warm inflation models, we show that the scaled framework suppresses numerical artifacts, improves the robustness of the deterministic evolution, and yields substantial computational speedups while preserving accuracy. We further show that correlated thermal noise contributions arise naturally through the diffusion matrix structure, resolving previously observed discrepancies between stochastic and deterministic implementations. Our results establish DSWIM as a numerically robust and computationally efficient framework for computing warm inflation scalar perturbations.

We study the role of Weyl symmetry breaking in conformal gravity and the residual scale symmetry of Einstein gravity. The corresponding action is characterized by a dimensionless coupling $\alpha$, determined by the ratio between the de Sitter and Planck scales. We show that this quantity admits a natural interpretation as the Bekenstein-Hawking entropy of de Sitter spacetime. Combining ideas from the functional renormalization group, holography, and emergent gravity, we propose a microscopic interpretation of $\alpha$ as a measure of the degrees of freedom associated with the de Sitter horizon. In this framework, the renormalization group flow of $\alpha(k)$ encodes the scale dependence of these microscopic degrees of freedom. Requiring this flow to be monotonically increasing toward the infrared leads to a cosmological constant of the same order as the observed one, suggesting an entropic solution to the old cosmological constant problem. This remarkably small value can therefore be understood as a direct consequence of the extraordinarily large number of degrees of freedom in our de Sitter universe.

We prove the Riemannian positive mass theorem in all dimensions for asymptotically flat $L^\infty$-metrics with subcritical singular sets. More precisely, we consider complete asymptotically flat manifolds whose metrics are smooth away from a compact singular set of Minkowski dimension less than $n-3+\frac{2}{n}$, and whose scalar curvature is nonnegative on the regular set. We show that the ADM mass of each asymptotically flat end is nonnegative, and that the mass vanishes in some end only in the Euclidean case. For the rigidity statement, we require additionally that the Minkowski dimension of the singular set is not larger than $n-3+\frac{1}{n-1}$. This gives an asymptotically flat analogue of Schoen's codimension-three conjecture for positive scalar curvature. The proof combines a density theorem for singular asymptotically flat metrics, capacity estimates across the singular set, conformal blow-up inspired by Bi-Hao-He-Shi-Zhu [3], and a $\mu$-bubble dimension-descent argument adapted from Brendle-Wang [6].

In light of recent cosmological observations, we examine a generalized Chaplygin gas model with a redshift-dependent exponent as a framework for describing the dark energy and dark matter content of the Universe. Specifically, we treat this fluid as a single unified component and test it against late-time background observational data. We employ Type Ia supernova data, cosmic chronometers, and baryon acoustic oscillations from the second data release of the Dark Energy Spectroscopic Instrument. We perform a Bayesian analysis for parameter estimation and compare the model with $\Lambda$CDM. We find that the generalized Chaplygin gas provides systematically higher values of the combined likelihood; nevertheless, once the larger number of free parameters is taken into account, both the Bayesian evidence and the Akaike Information Criterion suggest that the model is statistically indistinguishable from $\Lambda$CDM.

We study the decay of de Sitter space into black holes whose horizons are dressed by BPS vortices of a $\mathrm{CP}^1$ action. The process is mediated by a regular Euclidean instanton obtained as a vortex-deformed generalization of the Nariai instanton. Its Euclidean geometry has the form $S^2\times\Sigma$, where $\Sigma$ is a compact surface whose geometry is shaped by the vortex configuration. The resulting decay rates are controlled by a discrete topological charge, showing that matter vortices open a new topologically organized family of decay channels for de Sitter space.

gwNRHME is a recently developed framework that seamlessly converts a multi-modal (i.e with several spherical harmonic modes) quasi-circular waveform into multi-modal eccentric waveform if the quadrupolar eccentric waveform is known. Here, we employ the gwNRHME framework to combine a multi-modal quasi-circular waveform model NRHybSur3dq8 and quadrupolar non-spinning eccentric waveform model EccentricIMR to construct multi-modal non-spinning eccentric model NRHybSur3dq8-gwNRHME. Using a total of 35 eccentric numerical relativity (NR) simulations obtained from the SXS and RIT catalogs, we demonstrate that NRHybSur3dq8-gwNRHME model predictions agree well with NR (with typical relative $L_2$ errors of ~0.01 for the dominant quadrupolar mode) for mass ratios $ 1 \leq q \leq 4$ and eccentricities up to ~0.2 measured about 10 cycles before the merger. To demonstrate the modularity of the gwNRHME framework, we further combine EccentricIMR with BHPTNRSur1dq1e4 model and develop a non-spinning eccentric models named BHPTNRSur1dq1e4-gwNRHME. Finally, we develop a different variant of these models by replacing EccentricIMR with EccentricTD. Both the gwNRHME framework and associated models are available through the gwModels package.

Using publicly available numerical relativity (NR) simulations for non-spinning eccentric binary black hole (BBH) mergers, Ref \cite{Islam:2024rhm} demonstrated that the eccentricity-induced modulations in the amplitudes and frequencies of different spherical harmonic modes are mutually consistent and can be modeled using a single time series modulation. We extend the validity of the results to all non-precessing binaries by using 83 NR simulations from the SXS, RIT, and MAYA catalogs for aligned-spin eccentric BBH mergers with mass ratios ranging from $1:1$ to $1:4$. Based on these phenomenological relations, we provide a framework named gwNRXHME to compute multi-modal eccentric non-precessing waveforms using two inputs: quadrupolar eccentric waveforms, and the corresponding multi-modal quasi-circular non-precessing waveforms. Furthermore, we compute an overall degree of departure in SXS, RIT, and MAYA NR data from these relations and find that SXS NR simulations generally adhere to these relations more strictly than RIT and MAYA data. We also show that these relations can offer a cost-effective way to filter out noisy higher-order spherical harmonic modes extracted from NR data. Our framework is publicly available through the gwModels package.

Characterizing eccentricity in gravitational waveforms in a consistent manner is crucial to facilitate parameter estimation, astrophysical population studies, as well as searches for these rare systems. We present a framework to characterize eccentricity directly from gravitational waveforms for non-precessing eccentric binary black hole (BBH) mergers using common modulations that eccentricity induces in all spherical harmonic modes of the signals. Our framework is in the spirit of existing methods that use frequency modulations in the waveforms, but we refine the approach by connecting it to state-of-the-art post-Newtonian calculations of the time evolution of the eccentricity. Using 39 numerical relativity (NR) simulations from the SXS and RIT catalogs, as well as waveforms obtained from the post-Newtonian approximation and effective-one-body (EOB) formalism, we show that our framework provides eccentricity estimates that connect smoothly into the relativistic regime (even up to $\sim 2M$ before merger). We also find that it is necessary to carry existing post-Newtonian calculations to an extra $0.5$PN order to adequately characterize existing NR simulations, and provide fits to the extra coefficient for existing simulations. We make the framework publicly available through the Python-based \texttt{gwModels} package.

Newtonian and post-Newtonian (PN) calculations suggest that each spherical harmonic mode of the gravitational waveforms (radiation) emitted by eccentric binaries can be further decomposed into several eccentricity-induced modes (indexed by $j=1$ to $j=\infty$), referred to as eccentric harmonics. These harmonics exhibit monotonically time-varying amplitudes and instantaneous frequencies, unlike the full eccentric spherical harmonic modes. However, computing or extracting these harmonics are not straightforward in current numerical relativity (NR) simulations and eccentric waveform models. To address this, Patterson \textit{et al} have developed a framework to extract the eccentric harmonics directly from effective-one-body formalism waveforms. In this paper, we build on the ideas presented in Patterson \textit{et al} and propose a data-driven framework, utilizing singular-value decomposition (SVD), that incorporates additional features based on PN intuition to ensure monotonicity in the extracted harmonics. We further demonstrate that the phase (frequency) of these harmonics is simply $j\phi_{\lambda}+\phi_{\rm ecc}$ ($jf_{\lambda}+f_{\rm ecc}$) where $\phi_{\lambda}$ ($f_{\lambda}$) is related to the secular orbital phase (frequency) and $\phi_{\rm ecc}$ ($f_{\rm ecc}$) is an additional phase (frequency) that only depends on the eccentricity. We also provide simple analytical fits to obtain the harmonics as a function of the mean anomaly. These relations may prove useful in constructing faithful models that can be employed in cheap and efficient searches and parameter estimation of eccentric mergers. Our framework is modular and can be extended for any other eccentric waveform models or simulation frameworks. The framework is available through the \texttt{gwMiner} package.

In this work, we investigate the gravitational wave emission from the periodic orbital motion of a test particle around two specific types of black holes in Einstein-Æther theory, a modified gravity that locally breaks Lorentz symmetry while remaining consistent with theoretical and observational constraints through a careful selection of its four coupling constants $c_i$. Focusing on the impact of the æther field, we examine the properties of periodic orbits, which are characterized by a set of three topological integers $(z, w, v)$ that uniquely classify their trajectories. We then calculate the gravitational waveforms generated by these periodic orbits, identifying potential observational signatures. Our analysis reveals a direct connection between the zoom-whirl orbital behavior of the small compact object and the gravitational waveforms it emits: higher zoom numbers lead to increasingly intricate waveform substructures. Moreover, the presence of the æther field introduces significant modifications to these waveforms, imprinting measurable deviations that could be potentially tested or constrained by future space-based gravitational wave detectors.

We consider various mechanisms of modifying the effect of intrinsic curvature in gravity with respect to General Relativity. Two primary approaches for suppressing intrinsic curvature are studied. First, by considering a Lagrange multiplier or an auxiliary field. Second, by non-minimal coupling between a scalar field and the intrinsic curvature scalar. We promote the foliation to a dynamical field, getting a fully covariant, and foliation independent theory. We reproduce the basic solutions of FLRW cosmology, black hole solutions, Lense-Thirring effect, and gravitational waves. The speed of gravitational waves is modified in comparison to the speed of light. A certain limit of our theory corresponds to the lowest-order Carroll gravity. Hence, our theory is a different UV completion of Carroll gravity, compared to the usual expansion of a small speed of light. Carroll gravity limit also has an enhanced symmetry, making the reduced or vanishing intrinsic curvature technically natural. Finally, our construction defines a one parameter family of theories, that sets the relative strength of the intrinsic and extrinsic curvature, and General Relativity corresponds to a specific value of this parameter.

In this paper, we reinvestigate the Starobinsky inflation model and its reheating features in light of the recent ACT results. To make the Starobinsky model consistent with the ACT data at the $68\%$ confidence level, the number of e-folds must increase while the reheating temperature decreases. We find that the Starobinsky model requires a spectator field to achieve efficient preheating. The preheating stage and the reheating temperature must be significantly adjusted to accommodate the lower temperature. In this paper, the favored non-minimal coupling of the produced particles is approximately $10$ or slightly lower. We also present viable parameter sets that fit the preferred reheating mechanism in this model. For certain parameter choices, the daughter fields could potentially be detected in future collider experiments such as the LHC or the ILC. Furthermore, our proposed mechanism can reproduce the lower reheating temperature, but it fails when the temperature falls below $1$ GeV.

Numerical relativity (NR) provides the most accurate waveforms for comparable-mass binary black holes but becomes prohibitively expensive for increasingly asymmetric mass ratios. Point-particle black hole perturbation theory (ppBHPT), which expands the Einstein equations in the small-mass-ratio limit, offers a computationally efficient alternative but is expected to break down in the comparable-mass regime because it neglects nonlinear effects. Nonetheless, several recent studies have shown that ppBHPT can model non-spinning binaries with high accuracy when supplemented by simple calibrations or a first post-adiabatic (PA) correction. Here we assess the applicability of ppBHPT to quasi-circular binaries with a spinning primary by comparing waveform amplitudes, orbital frequencies, and orbital phases. We find that spin effects in ppBHPT waveforms (without additional spin information beyond adiabatic order) are in surprisingly close agreement with the corresponding NR calculation (outperforming some post-Newtonian models) over the last $\approx 20$ orbital cycles. This suggests that, after incorporating higher-order corrections into ppBHPT waveforms in the non-spinning limit -- via second-order self-force results or semi-analytical fits -- only modest spin-dependent adjustments may be required to achieve NR-faithful ppBHPT waveforms. We also show that combining non-spinning NR information with adiabatic ppBHPT can provide a reasonably accurate inspiral waveform for spins $\chi \lesssim 0.5$ mass ratios $q \gtrsim 5$.

Modeling the remnant recoil velocity (kick) distribution from binary black hole mergers is crucial for understanding hierarchical mergers in active galactic nuclei or globular clusters. Existing analytic models often show large discrepancies with numerical relativity (NR) data, while data-driven models are limited to mass ratios of q<=8 (aligned spins) and q<=4 (precessing spins) and break down when extrapolated outside their training ranges. Using ~5000 of NR simulations from the SXS and RIT catalogs up to q=128 and ~100 black hole perturbation theory simulations up to q=200, we present two classes of models: (i) gwModel_kick_q200 (gwModel_kick_q200_GPR), an analytic (Gaussian process regression) model for aligned-spin binaries. (ii) gwModel_kick_prec_flow, a normalizing-flow model for kick distribution from precessing binaries with isotropic spins. Our approach combines analytic insights from post-Newtonian theory with data-driven techniques to ensure correct limiting behavior and high accuracy across parameter space. Both gwModel_kick_q200 and gwModel_kick_prec_flow are valid from comparable to extreme mass ratios. Extensive validation shows all three models outperform existing ones within their respective domains. Finally, using both back-of-the-envelope estimates and 1404 detailed star cluster simulations incorporating our kick models, we find that the black hole retention probability in low mass globular clusters can vary noticeably when the gwModel_kick_prec_flow model is employed. The models are publicly available through the gwModels package.

For millennia, humanity has relied exclusively on light$\unicode{x2014}$initially visible light and, later, broader and broader portions of the electromagnetic spectrum$\unicode{x2014}$to observe the universe. In the past decade, a remarkable chapter in extending astronomy beyond electromagnetic antennas has been concretized: the dawn of gravitational-wave astronomy has opened a new observational window into the cosmos. Among the many new astronomical sources we may now look for and study through their gravitational-wave signals, the Big Bang is surely among the most fascinating. Gravitational waves give us concrete hope of directly observing the primordial universe, whose light, emitted more than 13.7 billion years ago, is blocked from reaching our telescopes. This dissertation is aimed at the study of gravitational waves from cosmic inflation, the main scientific paradigm for the very early universe. Therefore, the text is divided into chapters on gravitational waves, inflationary cosmology, and inflationary gravitational waves. More specifically, our discussion will be steered by the endeavor to explain how the gravitational-wave signal sought by the NANOGrav observatory could have originated in the primordial universe.

We study the quantum dynamics in Krylov space of a spatially flat, homogeneous, and isotropic universe sourced with a massless scalar field within Wheeler-DeWitt (WDW) quantum cosmology and loop quantum cosmology (LQC) frameworks. The availability of a physical Hilbert space and physical Hamiltonian and the presence of an internal clock enable us to construct the Krylov basis analytically by applying the Lanczos algorithm. We then evaluate both the Krylov state and operator complexity for WDW quantum cosmology and LQC on this basis. In regimes where the wave function of the universe is sharply peaked, our results indicate that the Krylov complexity grows quadratically with the scalar field clock for the state and operator complexities in both the WDW quantum cosmology and LQC. We further show that the operator complexity is exactly twice the state complexity in these regimes. We discuss the interpretation of the global behavior of these systems by calculating the Krylov entropy for both quantum cosmological frameworks. We observe that in LQC, the Krylov complexity and entropy remain finite at the bounce, whereas in the WDW quantum cosmology, they diverge at the big bang/crunch singularity. Our work provides the first example of computing Krylov complexity for a system with a totally constrained Hamiltonian and no external time, a framework to calculate a purely quantum-mechanical entropy in quantum cosmology, and, to our knowledge, the first direct bridge between Krylov complexity and canonical quantum cosmology, as a first step toward understanding how polymerized quantum geometry modifies complexity and entropy.

We present a comprehensive analysis of late-time tails in gravitational radiation from merging spin-aligned eccentric binary black holes, using high-accuracy point-particle black hole perturbation theory simulations. We simulate the late-time evolution of 15 binary black hole mergers with mass ratio $q = 1000$, dimensionless spins $\chi = [-0.9, -0.6, 0.0, 0.6, 0.9]$ and eccentricity at the last stable orbit $e_{\rm LSO} = [0.8, 0.9, 0.95]$. We track the tail amplitudes and exponents up to a retarded time coordinate $t = 9000M$ after merger for the six spin-weighted spherical harmonic modes $(2,1)$, $(2,2)$, $(3,2)$, $(3,3)$, $(4,3)$, and $(4,4)$ employing both frequentist and Bayesian approaches. We note that the tails are increasingly pronounced for binaries with high eccentricity $e_{\rm LSO}$ and large negative spin $\chi$. We find that the overall late-time exponents closely approach their predicted asymptotic values ($p=-\ell-4$ for Weyl curvature scalar $\psi_{4,\ell m}$ where $\ell$ is the spin-weighted spherical harmonic index), while estimates restricted to the latest portion of the data exactly recover them. We further verify numerically that modes with the same spherical index $\ell$ share identical tail exponents, while variations in $m$ do not affect the tail behavior. Our analysis framework is publicly available through the gwtails Python package.

We revisit an analytical approximation scheme for computing nonlinearity ratios involving quadratic quasinormal modes (QQNMs). We compute these ratios for the general case when the QQNM is not one of the linear QNMs, for the $(l,m)$ channel $(2,2) \times (2,2) \to (4,4)$. We find an excellent match with numerical simulations. We also discuss where and why the method can fail, for example, for the channel $(2,0) \times (2,0) \to (2,0)$ where we can only get crude estimates for the nonlinearity ratio. Motivated by recent studies on nonlinear ringdown at the horizon, we also compute the nonlinearity ratios at the horizon. We find that the ratio both at the horizon and infinity is insensitive to different choices of regularization of the source term in the second order perturbations. We also discuss amplitudes of QQNMs sourced by linear overtones. Finally, we discuss the issues that must be resolved within this method to do precision analysis of nonlinear ringdown.

The study of periodic orbits in extreme-mass-ratio inspirals is essential for understanding the dynamics of small bodies orbiting supermassive black holes. In this paper, we study the periodic orbits and their corresponding gravitational wave emissions within the framework of an effective field theory-based extension of general relativity (EFTGR), which incorporates higher-order curvature terms into the Einstein-Hilbert action. We start with a brief analysis of the modified black hole spacetime in EFTGR and examine how its parameters influence the dynamics of a massive neutral particle using the Lagrangian formalism. Focusing on the impact of the higher-order curvature terms in EFTGR, we examine the properties of periodic orbits, which are characterized by three topological integers $(z, w, v)$ that uniquely classify their trajectories. By analyzing these orbits within EFTGR, we aim to provide new insights into how strong-field deviations from general relativity may manifest in observable phenomena. We then calculate the gravitational waveforms generated by these periodic orbits, identifying potential observational signatures. Our analysis reveals a direct connection between the zoom-whirl orbital behavior of the small compact object and the gravitational waveforms it emits: higher zoom numbers lead to increasingly intricate waveform substructures. The results contribute to a clearer understanding of the dynamical features of EFTGR and open new avenues for probing black hole properties via gravitational wave detection.

We investigate the impact of Lorentz violation on the compactness of mini-boson stars and the resulting gravitational-wave signals from extreme-mass-ratio inspirals (EMRIs) within the framework of bumblebee gravity. Numerical solutions for static, spherically symmetric configurations reveal that a positive Lorentz-violating parameter $\ell$ suppresses repulsive pressure, thereby enhancing gravitational binding and yielding more compact boson stars. Conversely, a negative $\ell$ amplifies repulsive pressure and weakens gravitational binding, such that no static solutions exist beyond a critical negative value. These structural modifications imprint distinct features on EMRI dynamics, characterized by a monotonic decrease in both orbital eccentricity and radial range as $\ell$ gradually increases from negative to positive values. Unlike the intermittent bursts from grazing orbits that resemble black-hole signals, penetrating orbits that enter the boson-star core exhibit sustained, amplitude-modulated gravitational-wave signatures without quiet intervals. Their characteristic strain falls within the detectability range of LISA, providing a potential observable for constraining Lorentz violation.

The Newman--Penrose (NP) formalism is traditionally used to analyze the polarization content of gravitational waves, while the gauge-invariant Bardeen formalism provides a complementary, and often simpler, description based on the irreducible scalar, vector, and tensor perturbations of the metric. In this work we apply the Bardeen formalism to plane gravitational waves in Minkowski spacetime, computing all scalar, vector, and tensor gauge-invariant variables explicitly and demonstrating that only the two transverse-traceless tensor modes survive, as expected for vacuum waves in general relativity. We then compare these Bardeen variables with curvature-based invariants constructed using the linearized Cartan--Karlhede (CK) algorithm. Although one might anticipate a correspondence, our analysis shows that the CK invariants do \emph{not} capture the polarization modes: the Weyl tensor possesses only a single non-zero Newman--Penrose scalar and the CK algorithm terminates without producing invariants that distinguish the $\oplus$ and $\otimes$ states. However, by computing invariant quantities obtained from the translational Killing vector fields of the Minkowski background that are retained under linear perturbation, we provide an algorithmic approach that reproduces the same physical tensor degrees of freedom captured by the Bardeen variables.

Black holes are spacetimes that should describe the end state of the gravitational collapse of huge amounts of quantum matter. A quantum description of dust cores for black hole geometries that accounts for the large number of matter constituents can be obtained by quantising the geodesic motion of dust particles and finding the corresponding many-body ground state. We here generalise previous works in spherical symmetry to rotating geometries and show the effect of angular momentum on the size of the core and effective interior geometry.

This study evaluates the capability of future multi-band observations of gravitational waves emitted from binary black hole coalescences, utilizing joint third-generation ground-based (CE, ET) and space-based (LISA, Taiji, TianQin) detector networks, to constrain parity and Lorentz symmetry violations in the gravitational sector. We model these effects through a parameterized waveform framework that incorporates a set of parameters that quantify potential deviations from general relativity. The frequency-dependence of their effects is described by power-law indices $\beta$ (i.e., $\beta_{\bar \nu}$, $\beta_{\bar \mu}$, $\beta_{\nu}$, and $\beta_{\mu}$). By analyzing events such as a high-signal noise ratio (SNR) "golden event" like GW250114 and a massive binary system like GW231123 (total mass $190-265 M_\odot$) using two networks of ground- and space-based detectors, we demonstrate that multi-band observations can significantly improve the current constraints on Lorentz and parity violations by several order of magnitude, for both high-frequency ($\beta > 0$) and low-frequency ($\beta < 0$) modifications. Our Bayesian analysis reveals that while the exceptional SNR of the GW250114-like event yields superior constraints for high-frequency modifications ($\beta > 0$), the massive nature of GW231123 provides more stringent limits for low-frequency effects ($\beta < 0$). This work highlights the critical value of future multi-band gravitational wave astronomy for conducting precision tests of general relativity across diverse binary populations.

Typical gravitational production of relics from amplification of inflationary perturbations assumes Bunch-Davies initial conditions, i.e. a vacuum with initially no particles. In this paper we investigate the impact of non Bunch-Davies initial conditions to the final abundance of relics, with particular attention to the parameter space where the total dark matter abundance is reproduced. We present a general framework for any initial condition, through which we show their non-trivial effect on both spectrum and late-time abundance. We argue that for particles whose source of conformal symmetry breaking comes only from a mass term (spin-1/2 fermions and conformally coupled scalars), the choice of initial conditions has little impact on the mass range relevant to dark matter. For other particles, e.g. the longitudinal mode of spin-1, we see a large deviation from the standard computation. We exemplify and quantify our results with an initial thermal state and a two-stage inflation scenario, highlighting that the total dark matter can be obtained for a wide range of masses.

We show that, within a broad stationary-axisymmetric class, Kerr-type separability and hidden symmetry arise as a local consequence of the Einstein equations. Without assuming separability, algebraic speciality, Killing--Yano symmetry, or global boundary conditions, we analyze stationary and axisymmetric geometries in a locally non-rotating orthonormal frame and impose a minimal local equilibrium condition, namely the absence of mixed energy-momentum fluxes. We find that the mixed Einstein equations enforce a rigid projective alignment between radial and angular sectors, uniquely characterized by a constant-Schwarzian constraint. This constraint yields a universal classification of local solutions into Möbius, exponential, and trigonometric branches, of which global regularity selects precisely the Kerr-type sector. In this sense, the kinematical core of Kerr geometry is already fixed locally, and the Schwarzian structure provides the local origin of Kerr rigidity.

We investigate non-metricity effects on electron scattering in metric-affine bumblebee gravity, where spontaneous Lorentz symmetry breaking is induced by a vector field acquiring a nonzero vacuum expectation value. Treating the affine connection as an independent variable and integrating it out leads to an effective description in which non-metricity modifies the dispersion relation of the bumblebee modes. From the full momentum-space propagator, we determine the pole structure that governs the interaction and construct the corresponding static Green function and interparticle potential. For a purely timelike background, the dispersion relation remains isotropic and produces a Coulomb potential with a uniformly rescaled effective coupling; consequently, the scattering amplitude preserves the Rutherford angular dependence, with the Lorentz-violating parameter entering only as an overall multiplicative factor. In contrast, a spacelike background induces anisotropy in the dispersion relation, leading to an orientation-dependent potential characterized by a quadrupolar modulation. This anisotropic structure propagates to the differential and integrated cross sections, introducing directional dependence while preserving the long-range character of the interaction. Finally, we consider phenomenological constraints from atomic physics. Hydrogen spectroscopy constrains the isotropic sector associated with the timelike configuration, whereas searches for anisotropies provide stronger limits on the quadrupolar contribution governed by $\xi b^{2}$.

This work investigates the universality of cusp formation in the shadows of compact objects. The emergence of cusps is accompanied by three interrelated phenomena: a topological charge transition, an equal-area law governing the self-intersecting structure, and universal critical scaling behavior. We demonstrate that, because these phenomena originate from the global morphology of the shadow, they are fundamentally independent of specific spacetime metric details and apply across diverse models. These features are systematically analyzed for the Kerr black hole endowed with a running Newton coupling. By extending our framework to rotating traversable wormholes, we confirm that the same universal behavior persists in more general compact objects. Our study uncovers the universality underlying cusp formation, offering a model-independent framework for characterizing possible non-Kerr shadow morphologies.

We study axial gravitational perturbations of a hairy black hole constructed in the framework of gravitational decoupling and investigate the geometric origin of echo-like late-time signals in this spacetime. We derive the odd-parity master equation and the corresponding effective potential, and we compute the quasinormal-mode spectrum by using frequency-domain and time-domain methods. We show that, in a suitable region of parameter space, the axial potential develops a double-peak structure that supports a trapping cavity and gives rise to echo-like late-time waveforms. Rather than imposing near-horizon reflectivity by hand, the delayed pulses therefore arise dynamically from the geometry of the effective potential. Our results provide a useful framework for probing black hole hair through gravitational-wave ringdown and for exploring possible observational departures from the standard no-hair paradigm.

In 1918 Weyl introduced Weyl conformal geometry and its associated quadratic action which was the first gauge theory, of the Weyl group (of dilatations and Poincaré symmetry). The initial physical interpretation of his theory was however short-lived and led to the downfall of Weyl geometry as a physical theory. We review how this action was re-born into a physical Weyl quadratic gauge theory of gravity. This is the only (quadratic) gauge theory of a spacetime symmetry with a physical gauge boson, is Weyl anomaly-free, has {\it exact} geometric interpretation, with all scales of geometric origin, and generates Einstein-Hilbert action and a positive cosmological constant in its Stueckelberg broken phase. A more fundamental Weyl gauge theory is the Weyl-Dirac-Born-Infeld (WDBI) action of Weyl geometry, that is Weyl gauge invariant in arbitrary $d$ dimensions and that does not need a UV regulator (!), of which the (geometrically regularised) Weyl quadratic gauge theory is the leading order. For $d=4$ the WDBI action can include SM operators alongside gravitational terms into a unified description, both geometric and by the gauge principle, of SM and Einstein-Hilbert gravity, which are recovered in the leading order of this action.

We study classical energy-condition admissibility for subluminal, positive-energy warp shells. For the constructions examined here, the energy-condition failures are localized at the smooth source--vacuum transition rather than in the bulk interior. We introduce two \emph{source-first} shell ans"atze whose metric potentials are obtained from the Einstein constraints for a prescribed matter model: a shift-free S-shell and a T-shell whose shift is derived from the momentum constraint. We assess them with a five-criterion standard comprising regularity, constraint satisfaction, an explicit matter model, frame-independent energy-condition margins, and global diagnostics; the standard responds to the source-consistency critique of Barzegar, Buchert, and Vigneron. Applied to eight constructions spanning the canonical warp-drive classes, none passes the full standard. An independent frame-independent verification of the Fuchs constant-velocity shell confirms interior energy-condition compliance (0 of 13 interior probes violate) but reveals Hawking--Ellis Type~IV violations in the smoothing tail beyond the nominal shell. A frame-independent scan over shell compactness and thickness (600 configurations) yields no admissible configuration in either source-first class. The same boundary deficit appears in the shift-free S-shell and persists in the static $v_0=0$ limit, which ties it to the transition geometry rather than to the shift. Along a representative off-axis null ray the null-energy line integral is nevertheless positive for every source-prescribed shell; this is an exploratory diagnostic rather than a proof of the averaged null energy condition, but it shows that the pointwise boundary failures need not appear in that integral.

The ring wormhole is the zero-mass limit of the Kerr metric. Its geometry is locally flat, but the topology is nontrivial, with a throat connecting two asymptotic regions and a distributional curvature singularity on the ring encircling the throat. We construct stationary generalizations of this static wormhole that are different from Kerr and invariant under reflections across the wormhole throat. The problem reduces to solving the vacuum Ernst equations subject to the corresponding symmetry conditions. The slowly rotating perturbative solutions were constructed previously, while we now present a detailed analysis of non-perturbative solutions obtained within a numerical framework. For slow rotation, they exhibit the non-relativistic relation $M\sim J^2$ between the mass and angular momentum, which transforms into the Regge relation $J=M^2$ in the fast-rotation regime, when $J\to\infty$ and the ring is stretched without bound by the centrifugal force. However, if the ring size in the static limit is sent to zero at the same time, then $M$ and $J$ remain bounded as the throat linear velocity approaches unity. The wormhole geometry then approaches the extremal Kerr solution, thus ``mimicking'' it. The wormholes carry a curvature singularity at the ring, but this can be removed by via simple ``scalarization'' procedure that promotes the vacuum solutions to regular wormholes with a phantom scalar field.

Much like the aerodynamic deflection of a spinning curveball, a rotating secondary in an extreme-mass-ratio inspiral (EMRI) experiences Magnus and lift forces, in addition to the standard drag force, when traversing a gaseous environment. We present the first framework that incorporates these specific spin-coupled environmental effects (EEs) into the evolution of EMRI. Over the multi-year observation windows of space-based gravitational-wave (GW) detectors, these interactions imprint a unique, distinguishable dephasing signature on the signal. Crucially, a Fisher matrix analysis reveals that gas drag breaks the fundamental vacuum-projection degeneracy between the secondary's spin magnitude and inclination, thereby tightening parameter constraints. Thus, accounting for EEs is not merely a modeling necessity, but could potentially be a powerful tool for enhancing the detectability of the secondary's intrinsic spin, and could serve as a novel probe of accretion flows harboring massive black holes.

We enlarged the capabilities of the publicly available Mathematica-based tool $\tt GrayHawk$. This second version expands the spectrum of metrics that can be considered in two distinct and disjoined directions. First, it enables a fully numerical computation of the tortoise coordinates integral, allowing the user to account for many metrics for which an analytic computation was impractical. Second, it extends the scattering problem to wormhole solutions. The pool of pre-loaded metrics is enriched, enabling immediate testing of the new features, and the code's modular structure is maintained to facilitate easy modification. This implementation proves $\tt GrayHawk$ adaptability and makes it an even more powerful tool for studying black holes, wormholes, Hawking radiation, and other features involving field propagation on curved manifolds. The codes described in this work are publicly available at \href{this https URL}{\faGithub}.

We present $\tt BlackHawk$ $\tt v3.0$, a major update of the public code designed to compute Hawking radiation spectra of black holes. Building upon previous versions, this release considerably extends the range of black hole geometries that can be studied by implementing several new spherically symmetric metrics: the Bardeen and Hayward regular black holes, the Simpson-Visser and Peltola-Kunstatter black-bounces, the D'Ambrosio-Rovelli black hole-to-white hole metric, and the Babichev-Charmousis-Lehébel black hole. For each metric, we compute the corresponding Hawking temperatures and greybody factors, enabling the determination of primary Hawking emission spectra for particles of different spins. The greybody factors are obtained through dedicated numerical routines based on the companion code $\tt GrayHawk$. Additionally, $\tt BlackHawk$ $\tt v3.0$ introduces several technical improvements aimed at enhancing precision and efficiency, providing a highly versatile tool. The code is publicly available at this https URL

The so called Harada gravity with non conserved energy-momentum tensor is here taken into account. It includes Rastall gravity as a special case. The field equations are written as Einstein equations where the source is supplemented by a divergence-free conformal Killing tensor and a tensor proportional to the metric, linear in the scalar curvature and the trace of the energy-momentum tensor. These terms can be natural candidates for dark sector and give rise to a coupling of the dark sector with the matter content. The field equations are the conformal Killing extension of Rastall gravity, and include Unimodular gravity. In a Friedmann-Robertson-Walker background, the Cosmic Microwave Background restricts parameters so that the dark sector only couples with the trace of the energy-momentum tensor. The explicit form of the tensor for the dark sector is found, and the Friedmann and continuity equations are presented, with a standard cosmological analysis. The sum of energy-momentum tensors of dust matter and of dark fluid is conserved, and the dust energy density evolves with the scale function with exponent -3/(1+tau), modified by the coupling tau with the dark fluid.

The geometry of the Einstein Telescope, the proposed next-generation European gravitational-wave observatory, is yet to be finalized. Two competing designs are under consideration: a nested triangular configuration (ET-{\Delta}) and two separated L-shaped detectors (ET-2L). Extensive prior comparisons of ET designs established the scientific landscape using the Fisher-information-matrix formalism and identified that duty-cycle-induced single-detector operation is precisely the regime where this approximation becomes less reliable, underscoring the need for a refined, principled treatment of the duty cycle. In this manuscript, we build on that foundation by revisiting the comparison with full Bayesian parameter estimation of gravitational-wave signals from binary black-hole mergers, projected onto a simulated Einstein Telescope that incorporates a refined duty cycle modelled via continuous-time Markov chains and testing different detector maintenance strategies. We find that the redundancy inherent in the ET-{\Delta} design enables it to maintain at least two operational detectors for the majority of the observing time, whereas the ET-2L configuration is often limited to a single detector. Crucially, we show that, during partial network operation, ET-{\Delta} often outperforms ET-2L, and that the increased multi-detector uptime translates into tighter constraints on the luminosity distance and source-frame component masses. Notably, this remains true even when gravitational-wave events have a lower signal-to-noise ratio in ET-{\Delta} than in ET-2L.

A quantum clock cannot be modeled as a point mass moving along a single geodesic if it is in a state with nonzero position fluctuations. Instead, it is an extended object subject to tidal forces and a superposition of time dilations at different altitudes. Here, a geometrical formulation of quantum mechanics is used to show that additional quantum properties representing correlations between different directions imply a non-Riemannian geometrical structure experienced by a quantum clock. A specific version of Finsler geometry parameterized by entropy and purity of the state provides a novel setting for a combination of quantum and gravitational effects. A crucial ingredient is given by a new parameterization of quantum-information properties related to second-order moments of a state and may also be useful in other applications.

We discuss the equations that arise from a Higgs--Yang-Mills dark sector coupled to gravity on a flat Friedmann-Lemaitre-Robinson-Walker metric. We choose the simplest $SU(2)$ representation, which we show to be compatible with the Cosmological Principle. We devise a multiple time scale approach to solve the equations of motion through a hierarchy of the couplings, utilizing exact solutions in terms of Jacobi elliptic functions. This novel method implements the dynamical system approach used in the literature and can shed new light on the possibility that this model can describe dark energy.

A quantum object is extended by virtue of uncertainty. When subjected to gravity, different parts of its wave function experience distinct local relativistic effects, leading to tidal and interference phenomena absent in the classical limit. These effects can be incorporated into a geometric extension of classical spacetime. For states quantum correlated in at least two directions, a complete description of motion requires a non-Riemannian geometry whose form is controlled by the state's entropy and purity and affects a broad range of phenomena from lab measurements to Hawking radiation. A specific implication of this framework is the appearance of quantum parameters in the time-dilation law in addition to the usual dependence on velocity and gravitational potential. The quantum-corrected time-dilation law is universal: the corrections depend solely on the external degrees of freedom and are independent of internal details of the clock mechanism.

A key test for any quasi-local energy in general relativity is that it be nonnegative and satisfy a rigidity property; if it vanishes, the region enclosed is flat. We show that the Hawking energy, also known as the Hawking mass, satisfies these properties under the dominant energy condition when evaluated on its natural area-constrained critical surfaces within a spacelike hypersurface (initial data set). In the time-symmetric case, these critical surfaces coincide with area-constrained Willmore surfaces, and we obtain positivity and rigidity theorems for the Hawking energy on such surfaces, including charged and cosmological constant (hyperbolic and spherical) variants as well as higher-dimensional analogues. In the fully dynamical (non-time-symmetric) case, we establish the first nonnegativity and rigidity theorems for the Hawking energy in this general setting. These results confirm the Hawking energy's consistency with basic physical principles and address several longstanding ambiguities and criticisms.

We theoretically propose a Hall effect driven by effective gravitational fields arising from quantum geometry. We identify four mechanisms for this ``emergent-gravity Hall effect'': real-space gravity, momentum-space gravity, gravitational anomalous velocity, and gravitational Lorentz force, all of which are described by Christoffel symbols in real, momentum, or time spaces. Based on the semiclassical theory, we construct a unified theoretical framework to systematically investigate how emergent gravity in these spaces affects transport phenomena. We demonstrate these effects through model calculations and clarify the conditions under which a finite Hall response can arise. Our findings open a new avenue for exploring gravitational effects in quantum systems.

We construct symmetry topological field theories (SymTFTs) using the sandwich construction of Pulmann-Ševera-Valach that manifest the centre symmetries of Chern-Simons theory and Yang-Mills theory as well as general relativity in the MacDowell-Mansouri formulation. The 'filling' of the sandwich is an AKSZ sigma model whose target space is a Weil algebra, augmented with discrete degrees of freedom given by a choice of topological boundary condition.

Recent DESI DR2 data has shown a significant preference for dynamical dark energy, yet this has further exacerbated the $H_0$ tension. In this work, we explore the potential of interacting dark energy models ($\widetilde{\Lambda}$CDM and $e\widetilde{\Lambda}$CDM) within the asymptotic-safety framework of quantum gravitational field theory to alleviate the $H_0$ tension. We perform observational constraints using the latest baryon acoustic oscillation data from DESI DR2, cosmic microwave background (CMB) data from Planck and ACT, and type Ia supernova data from DESY5 and PantheonPlus, as well as the SH0ES data. From our analysis, we observe the dynamical scale parameter of the cosmological constant, $\delta_{\Lambda} = -0.270\pm 0.100$, in the $e\widetilde{\Lambda}$CDM model using the CMB+DESI+SH0ES data, which deviates from $\Lambda$CDM at the $2.7\sigma$ level. Simultaneously, we find $H_0 = 70.84\pm 0.74~\mathrm{km\,s^{-1}\,Mpc^{-1}}$, reducing the $H_0$ tension to $1.7\sigma$. This increase in the inferred $H_0$ is due to the anti-correlation between $\delta_{\Lambda}$ and $H_0$, whereby a negative $\delta_{\Lambda}$ leads to a higher $H_0$ value. Furthermore, for the CMB+DESI+SH0ES combination, we obtain $\Delta\chi^2_{\min}=-14.14$ and $\Delta\mathrm{DIC}=-9.18$, favoring the $e\widetilde{\Lambda}$CDM model over $\Lambda$CDM. Overall, the $e\widetilde{\Lambda}$CDM model can improve the fit and ease the $H_0$ tension, especially for the data combinations that provide the strongest statistical support.

Spontaneous diffusion (i.e., non-conservation of energy) is a prominent, testable prediction of collapse and hybrid classical-quantum gravitational models. Without smearing of the mass density operator, the associated heating (or energy increase) rate diverges, yet the smearing distribution is arbitrary and, on scales much larger than the smearing length $r_C$, much of the phenomenology is expected to be insensitive to this choice. We propose to resolve this arbitrariness as follows: for a fixed $r_C$, select the distribution that minimizes the heating rate. Conceptually, this should identify the minimal deviation from standard quantum mechanics and provide models that, once experimentally refuted, would strongly disfavor all variants with different distributions. We apply this approach to the most investigated collapse models: GRW (for Ghirardi-Rimini-Weber), CSL (for Continuous Spontaneous Localization), and DP (for Diósi-Penrose). Notably, the Gaussian is optimal only for the GRW case. Finally, we apply it to the Tilloy-Diósi hybrid classical-quantum model of Newtonian gravity, leading to the minimally deviating variant of it. This version of the model is entirely determined by only one free parameter $r_C$ and, if experimentally refuted, would strongly disfavor any other version of it.

The dark bubble model makes a positive cosmological constant natural in string theory, and predicts several new physical phenomena within reach in the near future. In this paper we study the experimental consequences of the model for the strength of gravity at scales of order $10^{-5}$m. Contrary to other models of gravity involving extra dimensions, the dark bubble model predicts gravity to become weaker rather than stronger at small scales, compared to Newtonian gravity. In particular, we provide explicit predictions of measurable deviations using table top experiments. We also show how the same effect reduces the effective force of gravity at high energy densities in cosmology, leading to a period of early inflation without the need for anything beyond radiation. We also discuss the quantum origin of the universe with a 5D black hole acting as a catalyst for the nucleation of the dark bubble and how it accounts for the present matter content in the universe. This leads to a prediction of $\Omega_c \approx 5\times 10^{-4}$ for a positive curvature of the universe, suggesting an explanation of the why-now-problem of the cosmological constant. We end by speculating on how to incorporate AdS black shells as black hole mimickers within the dark bubble model.

We solve time-reversed stochastic inflation in the semi-infinite flat potential with a constant drift term and derive an exact expression for the probability distribution of the curvature fluctuations. It exhibits exponential decaying tails which contrast to the Levy-like power law behaviour encountered without friction. Such a non-vanishing drift acts as a regulator for the conventional ``forward'' stochastic $\delta N$-formalism, which is otherwise ill-defined in the unbounded and flat potentials typical of plateau models of inflation. This setup therefore allows us to compare the curvature distribution derived from both approaches, reverse and forward in time. Up to similar exponential tails, we find quantitative differences. In particular, in the classical-like limit of very large drift, the tails become Gaussian but only in the time-reversed picture. As a toy model of eternal inflation, we finally discuss the case of negative drift in which inflation never ends for many field trajectories. The forward approach becomes pathological whereas the reverse formalism gives back a finite curvature distribution with always exponential tails. All these differences end up being related to the very definition of the background which is ambiguous when a classical trajectory does not exist.

We define the perspective of any quantum reference frame (QRF) and construct reversible transformations between different perspectives. Our construction is based on two principles motivated operationally by the change from relative to absolute coordinates and leads to an incoherent group averaging approach with general symmetry group. Thereby, it extends the framework of [arXiv:2110.13199] from ideal QRFs, which generally require infinite resources like energy or angular momentum, to non-ideal QRFs, with only finite resources. We find that the perspective of a non-ideal QRF deviates significantly from that of an ideal QRF: Firstly, systems described relative to a non-ideal QRF appear superselected. Secondly, the structure of the perspective of a non-ideal QRF attests that successive relational operations on a system lead to back-reaction on this QRF.

We analyze the structure of one-parameter subgroups of SO(3,2). We find two new types of subgroups in comparison with the structure of the one-parameter subgroups of SO(2,2), and we construct explicit examples for these subgroups. We also comment on the placement of existing conformal gravity solutions within this classification.

We propose an infrared mechanism for alleviating the Hubble constant tension, based on a small departure from entanglement equilibrium at the cosmological apparent horizon. If the horizon entanglement entropy falls slightly below the Bekenstein-Hawking value, we parametrize the shortfall by a fractional deficit $\delta(a)$ evolving with the FLRW scale factor $a$. The associated equipartition deficit at the Gibbons-Hawking temperature then sources a smooth, homogeneous component whose density scales as $H^{2}/G$, with a dimensionless coefficient $c_{e}^{2}(a)$ of order unity times $\delta(a)$. Because this component tracks $H^{2}$, it is negligible at early times but can activate at redshifts $z\lesssim 1$, raising the late time expansion rate by a few percent without affecting recombination or the sound horizon. We present a minimal three parameter activation model for $c_{e}^{2}(a)$ and derive its impact on the background expansion, effective equation of state, and linear growth for a smooth entanglement sector. The framework predicts a small boost in $H(z)$, a mild suppression of $f\sigma_{8}(z)$, and a corresponding modification of the low-$z$ distance-redshift relation. We test these predictions against current low-redshift data sets, including SN~Ia distance moduli, baryon acoustic oscillation distance measurements, cosmic chronometer $H(z)$ data, and redshift space distortion constraints, and discuss whether the $H_0$ tension can be consistently interpreted as a late-time, horizon-scale information deficit rather than an early universe modification.

Using a combination of \textit{Hubble Space Telescope} and \textit{James Webb Space Telescope} imaging, a runaway supermassive black hole (RBH-1) was recently identified with an inferred velocity of $954^{+110}_{-126}\,\mathrm{km\,s^{-1}}$, likely ejected from a compact star-forming galaxy (denoted as GX) at $z \approx 0.96$. Assuming the runaway black hole was the outcome of the gravitational-wave-driven merger of two black holes, we use its measured runaway velocity together with gravitational-wave recoil predictions from numerical relativity and black hole perturbation theory to constrain the mass ratio and spin configuration of the progenitor SMBHs that overcame the final-parsec problem and merged $\sim 70$~Myr ago. We find that the progenitor binary must have been precessing, with a mass ratio $m_1/m_2\lesssim 6$, and that the more massive SMBH must have possessed a high spin (dimensionless spin magnitude $\sim 0.75$) in order to generate a recoil of this magnitude. This has important astrophysical implications as similar SMBH mergers can be an interesting source population for the upcoming LISA mission with signal-to-noise ratios $\gtrsim$ 1000. Furthermore, the progenitor SMBH properties imply that GX was likely formed through a major, gas-rich (``wet'') merger between two galaxies of comparable mass, with a mass ratio $\lesssim 4$.

In this work, we present an updated prescription of contemporary tidal dissipation theory adapted for rapid binary population synthesis. Our simplified expressions encode the dependence of tidal dissipation on stellar structure, stratification, and tidal forcing frequency, while remaining computationally efficient. We implement these prescriptions in the rapid population synthesis code COMPAS, and demonstrate the self-consistent coupling of tides with stellar evolution and binary properties such as orbital periods, spins, and eccentricities for several representative binary systems. When compared with commonly used tidal prescriptions, our equilibrium tidal dissipation efficiencies can be stronger by 1-2 orders of magnitude for low mass main sequence and giant type stars, and dynamical tides can be stronger by 1-7 orders of magnitude due to the explicit dependence on internal stellar structure and the presence of inertial wave dissipation. Despite our simplistic approach, our models agree with detailed stellar simulations to within an order of magnitude across tidal dissipation mechanisms.

It is well known that the diffusion equation, when treated as a stand-alone partial differential equation, exhibits exponential instabilities in boosted frames, which render the corresponding initial-value problem ill-posed. Recently, however, it was shown that Fick-type diffusion arises as the exact hydrodynamic sector of relativistic Fokker-Planck kinetic theory. In this work, we exploit this kinetic embedding to formulate a modified initial-value problem for one-dimensional Lorentz-boosted diffusion. We show that the resulting dynamics are well posed both forward and backward in time, provided the boosted density profiles admit a kinetic-theory realization. Such profiles form a space of band-limited functions, within which the evolution can be expressed as a discrete superposition of spatially sampled initial data, weighted by a Shannon-Whittaker-type Green function defined on the full Minkowski plane. The Green function is obtained in closed analytic form.

In Jackiw-Teitelboim gravity, the naive Schwarzian quantum mechanics leads to a continuous bulk spectrum, in apparent contradiction with the finite entropy of the black hole, which requires a discrete spectrum with level spacing of order $e^{-S_0}$. It was recently shown that restoring spectral discreteness with random statistics requires the introduction of a left confining potential that becomes relevant when the renormalized wormhole length reaches order $e^{S_0}$. In this work, we show how the known perturbative results of JT gravity are recovered within this modified framework. More importantly, we demonstrate that this modification has a direct dynamical consequence: it resolves the black-hole singularity. The confining potential generates a repulsive force at exponentially large wormhole length, preventing the indefinite growth that would otherwise lead to a singularity. We explain in detail how this turnaround arises and explore its implications for late-time bulk gravitational dynamics, the disappearance of horizons, and possible observational consequences.

In this paper, we explore the perturbative renormalization and study the classical dynamics of the bumblebee model coupled to quadratic gravity, a theoretical setting that allows the violation of Lorentz symmetry. Such a violation arises from a vector field whose potential is engineered to induce a nonzero vacuum expectation value (VEV), thereby leading to the emergence of a preferred direction in spacetime and, consequently, to the spontaneous breaking of Lorentz symmetry. Working in dimensional regularization and expanding the metric around flat space, we compute the one-loop divergent parts of the two-point functions of the bumblebee and graviton fields, with special emphasis on the role of Lorentz-violating insertions in internal lines. These results determine the counterterms required to renormalize the gravitational and bumblebee sectors in the presence of a preferred background direction, and make explicit how Lorentz-violating interactions feed back into the UV structure of quadratic gravity. On the classical side, we derive the field equations and identify exact solutions supported by bumblebee backgrounds. In particular, we show that the Schwarzschild and de Sitter geometries remain exact solutions for an appropriate bumblebee field profile, even in the presence of one of the non-minimal couplings. We close with a discussion of the operator content suggested by the one-loop structure and of prospective extensions to cosmological and less symmetric backgrounds.

Thermal correlators in holographic conformal field theories are known to exhibit singularities in complex time, sometimes referred to as ``bouncing singularities", which are believed to be related to bulk geodesics probing the black hole interior. These singularities correspond to exponentially suppressed contributions in the high-frequency limit of the thermal correlators. We revisit in detail the calculation of retarded two-point functions of local operators dual to bulk scalar fields in the planar AdS black hole background. We confirm that these correlators develop bouncing singularities, and highlight the agreement of two independent methods: a large frequency WKB analysis with infalling boundary conditions at the horizon; and an asymptotic OPE analysis that relies only on the near-boundary expansion, without any direct input from the black hole interior. We then extend these calculations to the case of the retarded two-point function of displacement operators on a Wilson line in the finite temperature gauge theory. This is computed holographically by solving the wave equation for the transverse fluctuations of the dual string worldsheet in the planar AdS black hole background. We find that these defect correlators also exhibit bouncing singularities, and again observe exact agreement between the WKB analysis sensitive to the black hole interior and the asymptotic OPE analysis. This agreement suggests that the bouncing singularities and the corresponding OPE data encode a universal high-frequency structure of the retarded correlators, and we propose a factorization formula that encodes the deviations from this universality.

We investigate the constraining power of future post-reionization and galaxy surveys on possible interactions between dynamical dark energy and dark matter. The analysis focuses on the interaction strength and the dark energy equation of state parameters, in addition to the six standard cosmological parameters. Using fiducial values obtained from the current observational bounds (Planck 2018 + DESI DR2 + Pantheon+), mock datasets for upcoming 21-cm intensity mapping, galaxy clustering and cosmic shear observations from the SKA-mid, and for the upcoming large-scale survey from the Euclid mission, were generated. Subsequently, Markov chain Monte Carlo analyses combining current cosmological data with these mock datasets were performed to forecast parameter constraints. The results indicate that both SKA-mid and Euclid observations can significantly improve constraints on interacting dark sector parameters. In particular, the interaction strength and dark energy equation of state parameters can be constrained considerably tighter than current combined constraints from Planck 2018, DESI DR2 and Pantheon+. Comparing different probe combinations and survey configurations, it is found that SKA2 provides the tightest projected constraints, particularly on the interaction strength, while Euclid achieves a precision broadly comparable to that of SKA1. The results highlight the potential of these upcoming surveys to probe interactions within the dark sector.

We develop a nonperturbative tensor-network framework for computing cosmological correlators in de Sitter space and use it to test the proposal that suitably defined in-in correlators can be obtained from an in-out formalism by gluing the expanding and contracting Poincaré patches. Focusing on interacting $1+1$-dimensional $\phi^4$ theory, we formulate finite-time lattice observables using Matrix Product State (MPS) techniques and analyze the regulator subtleties associated with the singular behavior near the patching surface. Within this regulated framework, we find controlled nonperturbative evidence for the proposed relation between in-in and in-out correlators in several examples. We also find suggestive evidence that the perturbative obstructions present for sufficiently light fields can be softened nonperturbatively, albeit in a regime of substantially larger entanglement. A central outcome of our analysis is an entanglement-based picture of the computation: for in-in evolution the entanglement remains modest and can decrease toward late times, whereas in the patched in-out set-up it grows significantly after the gluing slice. Thus, although the in-out formalism is perturbatively economical, the in-in formulation is numerically more favorable. We briefly discuss how the same strategy extends to low-angular-momentum sectors in $3+1$ dimensions, and why regimes of rapid entanglement growth may eventually motivate quantum-computing implementations.

The addition of Kounterterms to Einstein gravity leads to a finite action for asymptotically anti-de Sitter (AdS) spaces with a conformally flat boundary. In that sense, it provides a partial renormalization for AdS gravity when compared to standard holographic techniques, where the mismatch is given in terms of nontrivial conformal properties of the boundary. On the other hand, this method has the clear advantage that the variation of the action has a closed form in an arbitrary dimension. In this work, it is shown how to extract holographic information on conformal anomalies from the variation in $(2n+1)$-dimensional Einstein-AdS plus Kounterterms. Remarkably enough, a considerable part of the Weyl anomaly can be worked out for any odd dimension.

We study QED$_2$ in de Sitter space as a minimal interacting gauge theory in which cosmological expansion directly competes with quantum dynamics. In cosmic time, the hopping redshifts as $1/a(t)$ while the electric term grows as $g^2 a(t)$, sweeping the spectrum through a moving narrow-gap region in the $(\tau,m)$ plane. Exact diagonalization shows that this defines a pseudo-critical line governing the loss of adiabaticity, excitation growth, and redshifted response. Using matrix-product states at a fixed mass, we separate the fixed-cutoff thermodynamic limit from the continuum extrapolation. The late-time dip survives in the infinite physical box size limit, and shifts to later $\tau$ as the lattice spacing goes to zero, with current data favoring $\tau_* \approx 3.1$, while the dip depth remains less controlled. For Gibbs initial states, the same mechanism produces an irreversibility front in the relative entropy that tracks the pseudo-critical line and is detectable via LOCC-accessible observables. These results identify de Sitter QED$_2$ as a controlled setting for linking curved-space gauge dynamics, near-critical spectral structure, and operational irreversibility.

We infer recoil (kick) velocities for both individual binary black hole (BBH) mergers and candidate intermediate-mass black hole events, as well as for the BBH populations inferred from GWTC catalogs up to GWTC-5. We obtain informative recoil constraints for several events, including GW231028-153006 ($v_{\rm kick}=839^{+1018}_{-681}\,\mathrm{km\,s^{-1}}$) and GW231123-135430 ($v_{\rm kick}=974^{+944}_{-760}\,\mathrm{km\,s^{-1}}$), while finding that the majority of event-level recoil posteriors remain broad and only weakly informative. We further infer consistent population-level recoil distributions across GWTC-3, GWTC-4, and GWTC-5, with median kick velocities of approximately $300$--$330\,\mathrm{km\,s^{-1}}$. Using both event-level and population-level recoil estimates, we find typical retention probabilities of $\sim2$--$3\%$ for globular clusters, $\sim28$--$32\%$ for nuclear star clusters, $\sim25$--$29\%$ for dwarf galaxies, and $\sim92$--$94\%$ for elliptical galaxies. We also compute recoil-induced displacements and dynamical-friction return times, finding that retained remnants in globular clusters and nuclear star clusters can remain displaced from their host cores for extended periods. Our results show that retention alone is not sufficient to determine the prospects for hierarchical mergers: hierarchical-merger efficiency depends on both remnant retention and post-kick re-centering.

The AMPS firewall argument relies on treating early radiation, late outgoing Hawking modes, and interior partner modes as approximately independent quantum subsystems. In diffeomorphism-invariant quantum gravity, however, gravitational dressing and asymptotic constraints obstruct such a tensor-product factorization of physical observables. In this essay, we sharpen this obstruction by formulating subsystem independence directly in operator-algebraic terms. Using modular theory, half-sided modular inclusions along null directions, and the sector-wise maximality of the dressed radiation algebra at future null infinity, we show that -- within a fixed asymptotic charge sector -- the algebra associated with the interior Hawking partner cannot form an independent commuting subalgebra, but must be contained as a (non-commuting) subalgebra of the radiation algebra itself. The subsystem-independence assumption underlying the AMPS paradox therefore fails, and the entanglement-monogamy step never becomes applicable. As a result, unitary black hole evaporation and semiclassical horizon smoothness are compatible in asymptotically flat quantum gravity, without invoking entanglement islands, replica wormholes, or modifications of semiclassical horizon physics.

We further develop the proposal in Phys.\ Rev.\ Lett.\ \textbf{136} 071501 that interprets stochastic inflation as an open quantum system, by constructing the open effective field theory for the reduced density matrix of long wavelength modes. We clarify that this open effective field theory enjoys two renormalization group flows: the conventional Wilsonian channel, and a stochastic channel arising from the openness that has no counterpart in ordinary Wilsonian effective field theory. Focusing on the stochastic channel in the hard cutoff scheme, we identify both Gaussian and non-Gaussian diffusion as effective operators in the influence functional, and show that they are required by matching onto correlators and form factors of the perturbative full theory through a method-of-region in time. Beyond Gaussian order, the matching data are no longer local Wilson coefficients but nonlocal and non-Markovian Wilson kernels. We then obtain the bare Hamiltonian density of this open effective field theory and derive its nonlocal functional master equations, including the Fokker-Planck equation for the diagonal density matrix and the Klein-Kramers equation for the Wigner functional, with their zero-modess simplifications discussed. Finally, we take a first step toward a continuum version of this open effective field theory, replacing the hard cutoff by an analytic regulator in the stochastic channel, and demonstrate stochastic renormalization using a massive scalar as an example.

We give a proof of the cosmological splitting conjecture of Robert Bartnik from 1988, which expresses the rigidity of the cosmological Hawking--Penrose singularity theorem. It states that a timelike geodesically complete, globally hyperbolic spacetime which has compact Cauchy surfaces and satisfies the strong energy condition must split isometrically as a Lorentzian product. Our methods combine the construction of global viscosity solutions to the Lorentzian eikonal equation by Zhu--Wu--Cui with our recently developed elliptic approach to the proof of Lorentzian splitting theorems in joint work with Braun, Gigli and Sämann, where we make use of the $p$-d'Alembertian operator for $p < 1$.

We formulate stochastic inflation in an open quantum system framework. The field coarse-grained in a patch of fixed physical size, and the total momentum of that patch, form a canonical pair and act on a one-mode Fock space which we identify as the "bulk". At each time step, new comoving modes join the coarse-grained patch and the bulk has to be redefined. This redefinition produces an entangled mode that is traced over, yielding a non-unitary evolution equation for the bulk's density matrix. For a free test field in de Sitter, one obtains GKLS dynamics, generated by an effective Hamiltonian and a single non-Hermitian Lindblad operator, hence diffusion and Hubble friction originate from the same quantum channel. The Wigner-Weyl transform of the GKLS equation leads to a Fokker-Planck equation for the Wigner function, which matches the one that applies to the classical phase-space distribution of stochastic inflation. We also provide several schemes under which one can unravel the GKLS dynamics into stochastic Schrodinger equations when continuous measurements of the decoupled mode are performed, making contact with Langevin formulations of stochastic inflation. In the light-field regime, an additional overdamped reduction can be performed by integrating out the momentum variable in the Wigner distribution, leading to Starobinsky's slow-roll Fokker-Planck equation. In that regime, the purity of the patch is strongly suppressed. In contrast, for heavy fields, field diffusion is suppressed and the coarse-grained patch remains close to a pure underdamped oscillator, which prevents a classical stochastic treatment.

Primordial black holes (PBHs) in the asteroid-mass window ($10^{17}$-$10^{22}$ g) can account for all of the dark matter without violating any observational constraint, yet are routinely dismissed as fine-tuned. I put that dismissal to the test by applying three complementary fine-tuning measures uniformly across a broad landscape: three non-inflationary PBH production mechanisms, six classes of inflationary PBH models, and seven particle dark matter benchmarks, all evaluated against the same observable target. Three distinct naturalness universality classes emerge, determined entirely by the analytic structure of the abundance map rather than by the nature of the dark matter candidate. Biased-domain-wall PBHs are as natural as off-resonance weakly interacting massive particles and freeze-in particles; early-matter-domination and first-order phase transition PBH mechanisms occupy an intermediate tier alongside coannihilating WIMPs, unified by a structural identity in which the fine-tuning measure equals the logarithm of the ratio of the formation scale to the matter-radiation equality scale; and single-field ultra-slow-roll inflationary collapse is severely tuned for a distinct reason: a double exponential in which the power spectrum amplitude is itself exponentially sensitive to the inflaton potential coefficients, on top of the exponential collapse sensitivity of the abundance map. My main conclusion is that {\em the claim that PBH dark matter is generically fine-tuned conflates the worst case with a landscape spanning every naturalness tier}. The three-measure protocol also resolves a tension in the recent literature: the Barbieri-Giudice and Iovino-Riotto fine-tuning measures answer complementary questions and are reconciled within the two-layer decomposition developed here.

We study the one-loop correction to the entropy of near-extremal black holes in three-dimensional massive gravity at the special point where the theory exhibits a unique maximally symmetric vacuum and non-constant curvature hairy black holes can achieve extremality even in the static case. Focusing on the near-horizon AdS$_2\times S^1$ geometry, we evaluate the contribution of boundary graviton modes that become exact zero modes in the extremal limit. We show that the resulting one-loop partition function generates logarithmic corrections to the semiclassical entropy, providing a new extension to higher-curvature gravity of what has been recently obtained for near-extremal black holes in General Relativity.

We investigate the thermodynamic stability and the stochastic thermal fluctuations of the warped black hole solution in three-dimensional General Massive Gravity. We demonstrate that the black hole is thermodynamically unstable and identify the nontrivial Davies phase-transition curves from the behavior of its admissible heat capacities. Going beyond the classical stability analysis, we study thermal fluctuations within a modified finite-time nonequilibrium extension of Ruppeiner's Hessian-based fluctuation theory. For a class of isentropic and isoenergetic processes, we derive exact on-shell angular momentum trajectories in the thermodynamic state space and compute the corresponding thermodynamic lengths. These quantities characterize relaxation processes between macrostates and provide an estimate of the associated relaxation times. Furthermore, we show that the thermodynamic geodesic equations do not admit constant-angular-momentum solutions, suggesting a continuous change of the black hole's angular momentum. Our results consistently reproduce the warped AdS$_3$ black hole limit of Topological Massive Gravity.

Color graphs and their subgraphs, referred to as bubble graphs, correspond bijectively to the simplicial complexes of pseudomanifolds and their subsimplices, respectively. In this paper, we introduce matrix representations for colored graphs and their associated bubble graphs. By using this correspondence, we define simplicial-complex matrices and subsimplex matrices that encode the simplicial complexes of pseudomanifolds and their subsimplices. Moreover, we formulate mutation and crossover operations on colored graphs. Through the established correspondence among simplicial complexes, colored graphs, and simplicial-complex matrices, we extend these operations to simplicial complexes and simplicial-complex matrices. We further implement an algorithm generating simplicial-complex matrices and a genetic algorithm performing mutation and crossover of them to produce pseudomanifolds exhibiting diverse topologies. In addition, we implement procedures for decomposing the generated simplicial-complex matrices into simplex matrices, reconstructing the simplicial complexes of the associated pseudomanifolds from this information, and computing geometric quantities such as the volume, circumcenter, and dual-simplex volume of each simplex.