According to the GEVAG (Generalized Entropy Varying-G) framework, any modification to the Bekenstein-Hawking area law would also lead to a varying-$G$ gravity theory in which the effective gravitational constant $G_\text{eff}$ becomes area-dependent. Among a myriad of generalized entropy functions explored in the literature, of special interest is the logarithmic correction of quantum gravity. In this work, we apply GEVAG to investigate the effect of logarithmic correction on very early-time cosmology, including the conditions for inflation. We found that if the coefficient of the logarithmic correction term is negative, $G_\text{eff}$ becomes twice that of the current value; whereas, a positive coefficient leads to a very small value of $G_\text{eff}$, which may ameliorate the "arrow of time" problem. In fact, slow-roll inflation becomes more natural in the latter case. We make some comparisons with the constant-$G$ approach and reveal the advantages of the GEVAG approach. For example, it can evade the sudden singularity that could otherwise arise when the coefficient of the logarithmic correction term is negative. We also check the validity of the generalized second law and comment on the range of the various parameters.

In this work, we investigate the coupling of General Relativity with Nonlinear Electrodynamics (NED), governed by a general Lagrangian $\mathcal{L}(\mathcal{F})$, to address the axial singularity of four-dimensional black strings. Through a model-independent analysis, we scrutinize the viability of regular configurations by extending no-go theorems, originally formulated for spherical spacetimes, to cylindrical symmetries. We provide a comprehensive mathematical proof that regular, purely electric black strings cannot be generated by any NED Lagrangian that recovers the Maxwell limit in the weak-field regime, establishing a fundamental constraint for cylindrical topologies. Despite these limitations, we employ specific mathematical frameworks to construct new exact solutions for black strings, including cylindrical analogues of the well-known Bardeen and Hayward regular black hole classes. Each solution is analytically derived, and we demonstrate that their curvature invariants remain finite everywhere, effectively replacing the axial singularity with a regular core. Furthermore, we evaluate the physical consistency of these new metrics by subjecting them to stringent causality and unitarity constraints. Our results provide a comprehensive classification of the conditions under which NED can regularize cylindrical spacetimes and offer new insights into how topological differences between spherical and axial symmetries influence the global structure and the physical viability of non-singular gravitational objects in nonlinear gauge theories.

We examine the validity of classical energy conditions in nonsingular bouncing cosmological solutions arising in quadratic curvature gravity minimally coupled to a scalar field. Focusing on the null, weak, strong, and dominant energy conditions, we perform a systematic analysis under two distinct formulations of the energy-momentum tensor. In the first approach, the energy-momentum tensor is assumed to be sourced solely by the scalar field, whereas in the second, an effective energy-momentum tensor is constructed that incorporates the higher-curvature corrections characterizing deviations from general relativity. Our results reveal that, in the scalar-field description, the null, weak, and dominant energy conditions remain satisfied throughout the cosmological evolution, while the strong energy condition is necessarily violated during the bounce phase, enabling the avoidance of the initial singularity. In contrast, when the effective energy-momentum tensor is considered, all four energy conditions are violated near the bounce, highlighting the intrinsically non-Einsteinian nature of the underlying gravitational dynamics. These findings clarify the role of higher-order curvature terms in facilitating nonsingular cosmological bounces, providing important insights into the energy condition violations required in modified theories of gravity.

Oscillation modes of neutron stars, a key target for third-generation gravitational wave detectors, encode key information about their constituent nuclear matter. In this work, we study the effect of viscosity on oscillations of cold, polytropic, spherically symmetric neutron stars. We focus on purely radial oscillations and work perturbatively to linear order within two hydrodynamic frameworks: the acausal covariant generalization of the Navier-Stokes equations proposed by Eckart, and the causal generalization formulated by Bemfica, Disconzi, Noronha, and Kovtun (BDNK). We find that viscosity damps the radial modes on millisecond timescales and induces fractional shifts in the oscillation frequency which increase both with the compactness and viscosity of the star, reaching up to the percent level for the fundamental mode with bulk viscosities $\zeta\sim10^{30}\mathrm{g}/\mathrm{cm}/\mathrm{s}$. For more viscous stars, the oscillation frequency decreases, becoming zero (i.e., an overdamped mode) for $\zeta\gtrsim10^{31}\mathrm{g}/\mathrm{cm}/\mathrm{s}$. We also study the linear threshold of gravitational collapse. Consistent with recent analytic results in the small viscosity regime, we find that viscosity in Eckart theory cannot stabilize an unstable inviscid star. We provide numerical evidence that viscosity in BDNK theory is similarly unable to prevent gravitational collapse, but it slightly modifies the threshold of collapse. Overall, our results advance our understanding of the impact of viscosity on the oscillation modes of neutron stars, a key component of viscous asteroseismology with next-generation gravitational wave detectors.

We show that dynamical dark energy theories can imprint $O(1)$ modifications on the quasi-normal mode (QNM) spectrum characterising black hole ringdown. The time dependence of dynamical dark energy naturally gives rise to cosmological 'hair' around a black hole. Taking the cubic Galileon as a concrete example, which admits the only known stable solution of this kind, we parametrically connect the cosmological and black hole regimes, derive the induced QNM shifts and forecast the resulting dark energy constraints. We find that the dark energy field profile can be constrained with an accuracy of up to $10^{-2}$ for LVK and $10^{-4}$ for LISA.

Recently, for the first time, a metric of a static spherically symmetric generalized uncertainty inspired quantum black hole was derived. We apply the modified Newman-Janis algorithm to this metric and derive its rotating counterpart. We show that this metric has all the correct limits, while due to Newman-Janis side effects, the singularity which was resolved in the static case, is introduced back into the model. However, the slowly-rotating limit of this black hole is singularity-free. Furthermore, we show that the presence of quantum parameters modifies the location of the horizons, temperature, and entropy of the black hole, and allows the existence of naked singularities even if the ratio of the spin parameter to mass of the black hole is less than unity. Finally, by computing the shadow parameters of this black hole and comparing them with data from the Event Horizon Telescope for both M87* and Sgr A*, we set bounds on one of the quantum parameters of the model, and show that there is a limit on the angular momentum of M87* if this model is valid.

We analyze various gravity theories involving de-Sitter, quadratic $\mathcal{R}^2$ and non-minimally coupled scalar in the light of application of the Dyson-Schwinger technique involving exact background solution of the Green's function. We denote specific set of solutions for the metric to move towards a quantum analysis of the theory. This kind of solutions is identified as conformally flat metric. Such a conclusion naturally arises in the use of the Dyson-Schwinger equations in the study of the Yang-Mills theory through the mapping theorem. We show a sequence of cosmological phase transitions starting from the breaking of such conformal invariance that can be hindered by the presence of the non-minimal coupling.

We develop a comprehensive thermodynamic description for a zero-temperature boson gas in curved spacetime, integrating energy conservation with information-theoretic principles. Using the hydrodynamic Madelung representation within the ADM formalism, we establish two fundamental relationships: an energy balance equation representing the first law of thermodynamics from a spacetime perspective, and an information-theoretic constraint connecting Fisher entropy to the dynamical evolution of the boson density. This dual formulation clearly separates energy transport from information conservation while revealing how quantum information is preserved in curved backgrounds. The introduction of a stochastic velocity provides a bridge between quantum potential effects and underlying spacetime fluctuations, suggesting a gravitational basis for quantum stochastic behavior. We demonstrate the consistency of our framework through detailed analyses of quantum systems in both Minkowski and Schwarzschild spacetimes. This work provides a unified foundation for studying relativistic bosonic systems, with direct relevance to boson stars and scalar field dark matter models.

This study explores the bouncing solutions within the framework of modified $f(Q, L_m)$ gravity. We examine four prominent bouncing models, the symmetric bounce, super bounce, oscillatory bounce, and matter bounce, each of which has been extensively analyzed in the context of modified gravity theories. Our investigation focuses on the behavior of the Hubble parameter, the evolution of the scale factor, and the equation of state (EoS) parameters. Notably, the dynamics of the scale factor and Hubble parameter effectively support the bouncing scenario. During the bouncing epoch, the EoS parameters fall within the phantom region, reinforcing the viability of the bounce. To further validate the bouncing scenario, we assess the energy conditions associated with each model. Our findings reveal a violation of the null energy condition at the bouncing epoch, which successfully characterizes the model's bouncing behavior.

We revisit scalarized black holes in Einstein-scalar-Gauss-Bonnet gravity and analyze the thermodynamic phase transition between the Schwarzschild solution of general relativity and scalarized black holes. Restricting to spherically symmetric configurations, we investigate several classes of scalar-Gauss-Bonnet coupling functions. For the simplest quadratic coupling that triggers spontaneous scalarization, the scalarized solutions are thermodynamically disfavored and no phase transition occurs. For an exponential coupling, the phase structure depends strongly on the coupling parameter, allowing for the absence of a transition, a continuous second-order transition, or a discontinuous first-order transition. For couplings leading to purely nonlinear scalarization, we find either a first-order transition or no transition. These results reveal a rich phase structure of scalarized black holes controlled by the scalar-Gauss-Bonnet coupling.

Previous analyses of shocks generated by shell-crossing singularities are affected by inappropriate gauge choices, and no systematic method is available for selecting a consistent gauge. In this work, we develop such a method for effective quantum gravity coupled to a dust shell. We illustrate it in classical general relativity and verify it numerically, with results in agreement with the Israel junction condition. We also show that gauges such as the Painlevé-Gullstrand and Schwarzschild ones are incompatible with the presence of a dust shell when imposed on the whole spatial slice. This explains the difficulties in previous treatments. The framework developed here provides a basis for studying shell-crossing singularities and shock dynamics in generally covariant effective black-hole models.

This study provides an analytic and numerical characterization of a class of regular, asymptotically flat black holes described by a deformed static spherical metric. The model is grounded in a four-dimensional non-polynomial quasi-topological framework in which higher-curvature corrections remain dynamically nontrivial while the static spherical sector retains a reduced-order structure, enabling tractable black-hole solutions with regular cores. Starting from the existence conditions of horizons and regularity, the allowed parameter domain and the extremal bound are derived. Hawking temperature, shadow radius, photon-ring Lyapunov exponent, and ISCO binding efficiency are then analyzed across the physically allowed parameter space. We further extend the analysis to Novikov--Thorne thin-disk accretion by deriving the flux kernel, effective-temperature profile, and bolometric luminosity scaling, and by providing representative numerical datasets for these quantities. A coherent trend emerges: increasing the deformation parameter drives the solution away from Schwarzschild behavior, reducing temperature, shadow size, and photon-orbit instability rate while enhancing orbital binding efficiency and accretion luminosity; increasing the exponent $\nu$ suppresses deformation effects and restores Schwarzschild-like observables. These results provide a compact phenomenological map linking horizon structure, thermodynamics, optical signatures, dynamical instability, and thin-disk accretion diagnostics in this regular black-hole family.

We derive expressions for the first and second derivatives of the quintessence potential $V(\phi)$, in terms of $\lambda = -V^{\prime}/V$ and $\Gamma = (V^{\prime \prime}/V)/(V^\prime/V)^2$, as functions of the quintessence density fraction $\Omega_\phi$ and the cosmographic parameters $q$, $j$, and $s$. Our mapping is not explicitly a function of the equation of state parameter $w$. We use these results, along with recent observational data, to derive expansions of $V(\phi)$ about the present-day value of the scalar field, $\phi_0$.

We study the consistency of several early-Universe scenarios within a framework of non-minimal effective sca\-lar--ten\-sor gravity. We show that bounce, inflation, and genesis stages are supported within the aforementioned theory. Consequently, this framework can serve as a viable model of the early Universe, where accelerated expansion is driven by the theory's own intrinsic degrees of freedom. Notably, the theory also provides two different values of the Hubble parameter, potentially explaining the different values of the Hubble constant measured from galaxy clusters and relic radiation, respectively.

We provide a set of general tools to study the problem of stellar equilibrium in any gravitational theory in which spherically symmetric spacetimes satisfy master field equations taking the form of an equality between an identically conserved tensor, with derivatives of up to second order in the metric, and an identically conserved matter tensor. We derive the most general expression for the Tolman--Oppenheimer--Volkoff equation of stellar equilibrium that is compatible with these minimal requirements. A general discussion of the conditions that guarantee geodesic completeness at the center of symmetry is also presented. The equations of stellar equilibrium are integrated in a subset of the space of allowed deformations of general relativity proposed by Ziprick and Kunstatter, allowing us to illustrate universal aspects associated with the weakening of the strength of gravity, such as the mitigation of the Buchdahl limit obtained in general relativity or the existence of static solutions describing regular black holes with perfect fluid cores.

We analyze quasinormal modes, grey-body factors, and absorption cross-sections of a massive scalar field in four-dimensional Einstein--Gauss--Bonnet black-hole spacetimes within a stability-constrained coupling window. High-order WKB-Padé spectra show that increasing field mass typically reduces damping and drives the system toward long-lived, quasi-resonant behavior. The scattering sector follows the same potential-barrier physics: larger effective barriers suppress transmission and low-frequency absorption, while the Gauss--Bonnet coupling has a comparatively mild impact over the stable range. These results provide a compact baseline for massive-field spectroscopy in higher-curvature black-hole backgrounds.

Efficiently sampling from high-dimensional, multi-modal posteriors is a central challenge in Bayesian inference for astrophysics, especially gravitational-wave astronomy. Popular families of methods like Markov-chain Monte Carlo, nested sampling, and importance sampling all rely on proposal distributions to guide exploration. Because prior knowledge of the target is often limited, practitioners can adopt adaptive proposals that iteratively refine themselves using information gained from previously drawn samples. Traditional adaptive strategies, however, struggle in high-dimensional multi-modal settings: complex, non-linear correlations are hard to capture, and hyperparameters typically require tedious, problem-specific tuning. To address these issues, we introduce Parallel Adaptive Reweighting Importance Sampling (PARIS). PARIS models its proposal as a Gaussian mixture whose component centers are the existing samples and whose component weights match the current importance weights. New draws from the proposal therefore concentrate around high-weight regions, while candidate points in unexplored areas receive intentionally inflated weights. As the algorithm continuously reweights all samples up to the latest proposal, any initial over-weighting self-corrects once additional neighbor samples are collected. To enable rapid reweighting, we present an efficient update scheme and evaluate PARIS on illustrative toy problems and more realistic gravitational-wave parameter estimation tasks. PARIS achieves accurate posterior reconstruction and evidence estimation with substantially fewer function evaluations than competing approaches, highlighting its promise for widespread use in astrophysical data analysis.

We propose a novel model in which the Universe is created as a pair of coordinate-reversed counterparts, forming a globally CPT-symmetric system that permits local CPT violations within each sector. This framework naturally introduces a mirror universe with opposite chiralities and reversed microscopic time coordinates, providing a geometric interpretation of time reversal without relying on initial-final state interchange. We investigate the consequences of local CPT violation in each universe, which induces a mass difference between the real inflaton and anti-inflaton fields. Such an asymmetry can modify reheating temperatures and naturally generate the observed matter-antimatter asymmetry in both universes.

Given the recent interest in perspectival quantum reference frames (QRFs), we ask how quantum properties in the perspectival picture relate to their global, non-perspectival counterparts. It is instructive to establish this link, as most known results in quantum information theory are derived in the latter context. Specifically, we find sufficient conditions under which global entanglement decomposes into a combination of perspectival entanglement and coherence -- a phenomenon that we call entanglement transference. We apply this result to non-inertial QRFs, in particular, revisiting the problem of entanglement degradation. We find that entanglement degradation in the perspectival picture can be offset by an increase in coherence resources. The non-inertial problem may also provide clues to understanding perspectival QRFs in curved spacetime.

We present the first joint gravitational-wave cosmological inference with LISA extreme mass-ratio inspirals at $z\lesssim1$ (galaxy redshifts) and massive black hole binaries at $z\gtrsim1$ (electromagnetic counterparts). Combining these standard sirens reduces cosmological degeneracies and yields competitive constraints on the Hubble constant $H_0$ and the dark-energy equation-of-state parameter $w_0$. This highlights LISA's potential for late-time cosmology across a broad redshift range with systematics distinct from electromagnetic distance indicators.

We study non-perturbative quantum gravitational corrections to the thermodynamics and quantum work distribution of the $n$-dimensional Schwarzschild--Tangherlini--Anti-de Sitter black hole. Starting from the corrected entropy $S = S_0 + \eta\, e^{-S_0}$, where $S_0$ is the Bekenstein--Hawking entropy, we derive the modified specific heat, internal energy, Helmholtz free energy, and Gibbs free energy in closed form. The specific heat retains the classical divergence at $r_h^{*}=l\sqrt{(n-3)/(n-1)}$ for $n\geq 4$, but the quantum correction suppresses its magnitude by up to $78\%$ at small horizon radii. In the extended phase space, the uncharged black hole admits no van der Waals critical point; however, the non-perturbative correction induces a Hawking--Page transition for $n\geq 4$ that is absent in the semi-classical limit. The corrected Gibbs free energy turns negative at small $r_h$, opening a thermodynamic channel with no classical counterpart. Using the Jarzynski equality and Jensen inequality, we obtain the quantum work distribution during evaporation. The free energy difference $\Delta F$ between two black hole states undergoes a sign reversal at small horizon radii for $n\geq 4$ when $\eta=1$, flipping the average quantum work from negative to positive. This sign reversal grows with the spacetime dimension, reaching $\langle W\rangle \approx +4.31$ for $n=10$. These findings demonstrate that non-perturbative quantum gravitational effects qualitatively alter the phase structure and evaporation energetics of AdS black holes, and they cannot be captured by perturbative corrections alone.

Flavor oscillations in curved space-time provide a novel channel to explore the unknown parameters of neutrinos. In this work, the gravity-modulated CP violations (CPVs) in neutrino oscillations were investigated under the Reissner-Nordstrom, Hayward, and Simpson-Visser metric. The interplay among the CPV, the properties of neutrinos, and the space-time is illustrated with analytical and numerical methods. The morphologies of the flavor-oscillation curves show that the information on the mass-ordering, the absolute mass, and the gravitational parameters could be encoded into the amplitudes and periods of the CPVs. Hence, the characteristic of the space-time background may be identified through its modulation effects on the CPV, such as amplification, damping on the amplitudes.

We investigate the entanglement entropy of a massive scalar field using the spherical shell lattice model introduced by Das and Shankaranarayanan. A systematic numerical analysis is performed to study the dependence of the entropy on the field mass and on the size of the entangling region for both ground and excited states. For the ground state, we find that the entanglement entropy is exponentially suppressed by the field mass, reflecting the presence of a finite correlation length, while the geometric area-law scaling remains robust for all masses. For localized excited states, however, we uncover a qualitatively different behavior. The excess entropy does not exhibit universal scaling in the dimensionless variable mR. Instead, numerical results show that data points with identical mR but different (m,R) pairs do not collapse onto a single curve, demonstrating a clear violation of simple scaling. This breakdown is traced to the presence of an additional length scale associated with the finite width of the wave-packet excitation. This result identifies the coexistence of multiple infrared scales as a key feature of excited-state entanglement in massive quantum field theories. Mutual information provides an additional finite diagnostic of correlations in the chosen nested geometry. The numerical results show a strong dependence on the field mass, although the detailed behavior is sensitive to the geometric setup used in the calculation. These findings clarify how particle mass and excitation structure jointly determine entanglement properties, and suggest that the matter contribution to the generalized entropy in semiclassical gravity may depend on independent infrared parameters rather than on a single correlation scale. Implications for black hole entropy and the island formula are briefly discussed.

The standard weak lensing formalism assumes that the lensing map relating the observed image of a source to its intrinsic shape depends only on the deflection angle. We show that this description is incomplete beyond linear perturbation theory, even when only scalar perturbations are present at first order. Using the Jacobi map formalism, we derive expressions for the rotation field, shear B-modes, and their angular power spectra at second order in relativistic perturbation theory. In the standard formalism, rotation and shear B-modes share the same spectrum, however, this degeneracy is broken once the parallel transport of the Sachs basis is consistently taken into account. We quantify this correction numerically, finding a difference of about $5\%$ on large angular scales $\ell \sim 5$ for sources at redshift $z_\mathrm{s} = 0.5$. We also investigate frame-dragging effects, which are usually neglected in weak lensing. We present the first analytical derivation of the corresponding impact on the angular power spectrum of shear B-modes and show that it becomes the dominant contribution on scales $\ell \lesssim 10$. While both Sachs-basis rotation and frame dragging significantly affect shear B-modes on large scales, their effect on the observed galaxy ellipticity is of order $1\%$, making these nonlinear relativistic corrections challenging to detect in practice. Our results are supported by relativistic simulations of weak lensing observables, including the first numerical study of frame dragging in the power spectra of the lensing convergence and cosmic shear.

We prove a globally hyperbolic spacetime with locally Lipschitz continuous metric and timelike distributional Ricci curvature bounded from below obeys the timelike measure contraction property. The remarkable class of examples of spacetimes that are covered by this result includes impulsive gravity waves, thin shells, and matched spacetimes. As applications, we get new comparison theorems for Lipschitz spacetimes in sharp form: d'Alembert, timelike Brunn-Minkowski, and timelike Bishop-Gromov. Under appropriate nonbranching assumptions (conjectured to hold in even lower regularity), our results also yield the timelike curvature-dimension condition, a volume incompleteness theorem, as well as exact representation formulas and sharp comparison estimates for d'Alembertians of Lorentz distance functions from general spacelike submanifolds. Moreover, we establish the sharp timelike Bonnet--Myers inequality ad hoc using the localization technique from convex geometry. Alongside, we prove a timelike diameter estimate for spacetimes whose timelike Ricci curvature is positive up to a "small" deviation (in an $L^p$-sense). This adapts prior theorems for Riemannian manifolds by Petersen-Sprouse and Aubry to Lorentzian geometry, a transition the former two anticipated almost 30 years ago.

The detection of gravitational waves from a core-collapse supernova in the Milky Way or its vicinity represents a unique opportunity to probe the inner workings of these explosions. In this review, I briefly summarize our current understanding of the supernova explosion mechanism and then outline the physical processes that shape the supernova gravitational wave signal. The review highlights how the various components of the signal have the potential to constrain the progenitor rotation, the proto-neutron star structure, the nuclear equation of state, the nature of hydrodynamic instabilities, and the violence of turbulent motions in the supernova core. I also highlight some open questions and uncertainties in the theory of supernova gravitational wave astronomy as well as challenges for further progress. Specifically, there is a need to develop large model databases, systematic uncertainty quantification and methods for evidence assessment to prepare for multi-messenger observations from a Galactic supernova.

This article provides a gentle, visual introduction to the basic concepts of differential geometry appropriate for students familiar with special relativity. Visual methods are used to explain basics of differential geometry and build intuition for all types of Riemannian and Lorentzian manifolds of constant curvature. A visual derivation of the Thomas precession is given, showcasing the utility of differential geometry while also pointing a spotlight at certain intricacies of Minkowski space crucial from a pedagogical perspective. In addition, a straightforward method to generate some Carter-Penrose diagrams -- suitable for students with no differential geometry knowledge -- is presented, and a new method of indicating distortion on spacetime diagrams is shown.

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.

Dark energy is one of the deepest puzzles in modern cosmology, and mounting evidence suggests that it is not just a cosmological constant but a genuinely dynamical component. Although cosmology and dynamical systems theory emerged from different disciplines, dynamical systems methods have become essential tools to uncover the qualitative evolution of the universe. The equations governing homogeneous and isotropic cosmologies can be naturally written as systems of ordinary differential equations, making them an ideal arena for dynamical system analysis. This review begins with a sharp, streamlined introduction to the standard dynamical systems toolkit widely used in cosmology. We then move on to alternative formulations based on polar and hyperbolic variable transformations. These approaches unlock powerful new ways to probe a broad spectrum of scalar field dark energy models, to set and constrain initial conditions, and to analyze tracking behavior across wide classes of potentials. The review is self-contained, but consistently directs the reader to more specialized and in-depth treatments where needed.

Quantum field theory (QFT) on fractal spacetimes is a program aiming at quantizing the gravitational interaction consistently at all energy scales thanks to an intrinsically or dynamically induced multiscale or multifractal-like spacetime geometry that regularizes the infinities of standard QFT. We reach the goal of this program and formulate a field theory of quantum gravity which is shown to be super-renormalizable and unitary at all perturbative orders. Viable and unviable ways to test this proposal through black holes and gravitational waves are discussed.

Via constructing an explicit Lagrangian for which the perturbation equations are analogues of a scalar field propagating in a planar black hole space-time, it is found that all planar black holes conformal to a Painlevé--Gullstrand type line element can be realized as analogue metrics. We also introduce the concept of holographic entanglement entropy for planar black-hole space-times. This is valid for an arbitrary choice of conformal and blackening factor, thereby vastly extending the number of known examples of explicitly known analogue metrics.

We derive a general procedure for calculating the gravitational wave background (GWB) from cosmic string loops whose typical shape evolves over time, as in gravitational backreaction. Using the results of a large-scale study of numerical gravitational backreaction on Nambu-Goto cosmic string loops, we construct GWBs of backreacted cosmic strings for a range of tensions and frequencies of cosmological interest, and compare them to current and upcoming gravitational wave detectors. The GWBs are lower than prior predictions by anywhere from a few percent to around 30\%, depending on the frequency and tension in question.

We investigate three causality-violating spacetimes: Misner space (including Kip Thorne's "moving wall" model), the pseudo-Schwarzschild spacetime, and a new model introduced here, the pseudo-Reissner-Nordström spacetime. Despite their different physical origins -- ranging from a flat vacuum solution to a black-hole-type vacuum solution to a non-vacuum model requiring exotic matter -- all three share a common warped-product structure, $2$-dimensional cylindrical base metrics of Eddington-Finkelstein type, and fundamental causal features such as Cauchy and chronology horizons, acausal regions, and analogous geodesic behaviour. Building on a conjecture first proposed in 2016, we present a formal proof that the three models are pairwise isocausal on their universal covers and on suitable causally regular regions of their compactified forms. The proof is constructive, providing explicit causal bijections on the covers and identifying a concrete deck-equivariance criterion governing descent to the compactified spacetimes: if the equivariance degree satisfies $|k|=1$ the models are globally isocausal, whereas if $|k|>1$ or equivariance fails, then at most a one-way causal relation holds between the compactified models. These results supply a rigorous causal classification linking these spacetimes, placing them within a unified Misner-type family and providing a framework for extending the classification to other causality-violating solutions.

We study Primordial Black Holes (PBHs) formed by the collapse of rare primordial fluctuations during an early period of Matter Domination. The collapse threshold strongly depends on the shape of the peaks, decreasing as they become flatter and hence rarer. In the extreme limit of a top-hat perturbation, Harada, Kohri, Sasaki, Terada, and Yoo have argued that the growth of velocity dispersion prevents the formation of black holes unless the initial peak is larger than $\zeta_{\rm th} \sim \zeta_{\rm rms}^{2/5}$. Including the shape distribution of the peaks, we find that for a realistic cosmic abundance of PBHs, the effective threshold is larger, $\zeta_{\rm th} \sim \zeta_{\rm rms }^{1/10}$. And this model requires $\zeta_{\rm rms}\sim 10^{-1}$, which is much larger than the observed value at the CMB scales. Hence, PBH formation during Matter Domination is barely more efficient than Radiation Domination. We estimate the dimensionless spin parameter to be $a_{\rm rms} \sim \zeta_{\rm rms}^{7/4}\ll 1$, slightly larger than PBHs formed in Radiation Domination.

The expansion of the Universe in $f(R,T)$ gravity is studied. We consider functions of the form $f(R,T)=R+\lambda T^\epsilon$ where $\epsilon<1$. We find that for all models with $\epsilon<0$, the Universe transitions to exponential growth at late times, just as it does in the standard cosmological model, which corresponds to $\epsilon=0$. It also fits the type Ia supernova data slightly better than the standard cosmological model, without increasing the number of parameters of the theory. In contrast, the fits for $\epsilon >0$ rapidly become worse than the standard cosmological model.

We present a covariantly stable first-order framework for describing charge and heat transport in isotropic rigid media embedded in curved spacetime. Working in the Lorenz gauge, we show that the associated initial value problem is both causal and locally well-posed in the fully nonlinear regime. We then apply such framework to explore a range of gravitothermoelectric effects in metals undergoing relativistic acceleration. These include (1) the separation of charge through acceleration, (2) the non-uniformity of Joule heating across accelerating circuits due to time dilation, and (3) the effect of redshift on magnetic diffusion. As an astrophysical application, we derive a relativistic Thomas-Fermi equation governing the charge distribution inside a compact object, also accounting for Seebeck charge displacements driven by cooling.

Flexible and accurate noise characterization is crucial for the precise estimation of gravitational-wave parameters. We introduce a Bayesian method for estimating the power spectral density (PSD) of long, stationary time series, explicitly tailored for LISA data analysis. Our approach models the PSD as the geometric mean of a parametric and a nonparametric component, combining the knowledge from parametric models with the flexibility to capture deviations from theoretical expectations. The nonparametric component is expressed by a mixture of penalized B-splines. Adaptive, data-driven knot placement, performed once at initialization, removes the need for reversible-jump Markov chain Monte Carlo, while hierarchical roughness-penalty priors prevent overfitting. Validation on simulated autoregressive AR(4) data demonstrates estimator consistency and shows that well-matched parametric components reduce the integrated absolute error compared to an uninformative baseline, requiring fewer spline knots to achieve comparable accuracy. Applied to one year of simulated LISA X-channel (univariate) noise, our method achieves relative integrated absolute errors of $\mathcal{O}(10^{-2})$, making it suitable for iterative analysis pipelines and multi-year mission data sets.

We investigate FLRW cosmology in the framework of symmetric teleparallel $f(Q)$ gravity with a nonminimal coupling between dark matter and the gravitational field. In the noncoincidence gauge, the field equations admit an equivalent multi-scalar field representation, which we investigate the phase-space using the Hubble-normalization approach. We classify all stationary points for arbitrary function $f(Q)$ and we discuss the physical properties of the asymptotic solutions. For the power-law theory, we perform a detailed stability analysis and show that the de Sitter solution is the unique future attractor, while the matter-dominated point appears as a saddle point. Moreover, there exist a family of scaling solutions that can be related to inflationary dynamics. In contrast with uncoupled $f(Q)$ models, the presence of the coupling introduces a viable matter-dominated era alongside late-time accelerated expansion. Our study shows that the coupling function plays a crucial role in cosmological dynamics in $f(Q)$ gravity.

We consider the path-integral quantization of a minisuperspace cut-and-paste Lorentzian wormhole connecting two Minkowski spacetimes. The dynamics of the throat radius as a function of proper time is governed by a non-polynomial effective action derived by an application of the Israel junction condition formalism. Within a saddle-point approximation of the propagator describing the evolution from an initial to a final throat radius, we show that topology-changing transitions are suppressed by the Hessian determinant. In addition, we analyze the gravitational thermodynamics of the wormhole spacetime by a Wick rotation of the Israel-Lanczos equations in the presence of a thin-shell source. The resulting Euclideanized field equations are assumed to originate from a Euclidean effective gravity-matter action, which enters the path-integral representation of the gravitational canonical partition function. Therefrom we associate a temperature given by the inverse period of solutions, as well as a gravitational entropy as functions of the surface energy density and equation of state parameter of the shell. Both quantities are sourced entirely by the discontinuity of the extrinsic curvature across the junction. We show how this result can be applied to deduce a thermodynamic first law as the differential version of the conservation equation relating the effective mass of the shell to its surface pressure.

Hybrid metric-Palatini gravity unifies the metric and Palatini formalisms while preserving a propagating scalar degree of freedom, offering a compelling route to modified gravity consistent with current observations. Motivated by this success, we consider an extended framework -- the hybrid metric-Palatini scalar-tensor (HMPST) theory -- in which an additional scalar field $\phi$ modulates the curvature couplings, enriching the dynamics and enabling nontrivial self-interactions through scalar potentials. We focus on the analytically tractable linear-$f(\hat{R})$ subclass and study its cosmological, strong-field, and weak-field regimes. In homogeneous and isotropic settings, we identify de Sitter and matter-dominated cosmological solutions describing accelerated expansion and early-universe behavior. For static, spherically symmetric configurations, the field equations yield analytic solutions generalizing the Janis-Newman-Winicour and Buchdahl metrics, including the Schwarzschild-de Sitter limit. In the weak-field regime, linearized perturbations around Minkowski space lead to Yukawa-type corrections to the gravitational potential, with an effective Newton constant $G_{\rm eff}$ and post-Newtonian parameter $\gamma$ that recover General Relativity for heavy or weakly coupled scalars. These results show that the linear-$f(\hat{R})$ HMPST subclass provides a consistent and unified description of gravity across cosmological, astrophysical, and Solar System scales, offering a fertile framework for connecting modified gravity to observations and effective field-theoretic extensions.

The interaction of gravitational waves (GWs) with matter is normally treated as being insignificant. However, recent work has shown that the interaction with a viscous fluid may be astrophysically important when the distance between the matter and GW source is somewhat smaller than the GW wavelength. Previous work has mainly considered perturbations on a Minkowski background, and here these results are extended to the case that the background is a general, non-vacuum, static, spherically symmetric spacetime. Expressions are obtained for GW damping and the consequent heating of the fluid, and implemented in computer code. The results are applied to astrophysical scenarios: Core collapse supernovae, the post-merger signal from a binary neutron star merger, and matter accreting at a binary black hole merger. It is found that, compared to the Minkowski case, the damping and heating effects increase, in some cases by several orders of magnitude. It is possible for a GW signal to be completely damped, and for the heating to be such that a gamma-ray burst occurs.

We examine the observational discrepancies of two widely used models describing anisotropic (dark) matter distributions around a black hole, focusing on their photon spheres, shadow radii, and lensing observables. The models considered are the vacuum and Einstein cluster dark matter models, characterized by negative and zero radial pressure, respectively. The analysis reveals that these models display contrasting photon sphere behaviors. In particular, the Einstein cluster results in a more pronounced deviation in the shadow radius relative to the standard Schwarzschild black hole. Additionally, a distinctive lensing phenomenon associated with the matter halo is identified in both models.

It is argued that the previously proposed modification of the standard (flat) inflationary $\Lambda CDM$ model in which cosmological constant is replaced by thermal energy of expanding vacum, characterized by the Gibbons-Hawking temperature, explains the origin of notorious ``Hubble tension''.

In June 2023, multiple pulsar timing array (PTA) collaborations provided evidence for the existence of a stochastic gravitational-wave background (SGWB). As a significant source of the SGWBs, scalar-induced gravitational waves (SIGWs) receive extensive attention. We explore the influence of anisotropic primordial power spectra on second-order SIGWs and derive explicit expressions for the energy density spectra. For specific anisotropic inflation models, we analyze the impacts of Finslerian inflation and gauge field inflation models on PTA and the Laser Interferometer Space Antenna (LISA) and generalize the findings to model-independent scenarios. Our results indicate that current PTA observations cannot rule out the existence of small-scale anisotropic primordial perturbations.

In this work, we extend the standard cosmological model within the quadratic energy-momentum squared gravity (qEMSG) framework, introducing a nonminimal interaction between the usual material field ($T_{\mu\nu}$) and its accompanying partner field (qEMSF, $T_{\mu\nu}^{\rm qEMSF}$), defined by $f(\mathbf{T}^2)=\alpha\mathbf{T}^2$ with $\mathbf{T^2}=T_{\mu\nu}T^{\mu\nu}$. Adopting an analytical approach within the qEMSG framework, we present a comprehensive exploration of Big Bang Nucleosynthesis (BBN) dynamics. Our analysis selects the radiation-dominated universe solution compatible with the standard cosmological model limit as $\alpha\rightarrow0$ and reveals that qEMSF interaction model can modify the radiation energy density's evolution, potentially altering neutron-proton interconversion rates and consequently affecting $^4$He abundance in various ways. By explicitly defining modifications to the predicted primordial $^4$He mass fraction, $Y_{\rm p}$, we establish the most stringent cosmological constraints on the parameter $\alpha$ based on recent measurements of $Y_{\rm p}$: $(-8.81\leq\alpha\leq8.14)\times10^{-27}\,\mathrm{eV}^{-4}$ (68% CL) from Aver et al.'s primordial $^4$He abundance measurements, aligning with $\alpha=0$. Additionally, $(3.48\leq\alpha\leq4.43)\,\times 10^{-27}\rm{eV}^{-4}$ (68% CL) from Fields et al.'s estimates, utilizing the Planck-CMB estimated baryon density within the standard cosmological model framework, diverges from $\alpha=0$, thereby lending support to the qEMSF interaction model. The study also highlights the bidirectional nature of energy-momentum/entropy transfer in qEMSF interaction model, depending on the sign of $\alpha$. The implications of qEMSF in the presence of additional relativistic relics are also explored, showcasing the model's potential to accommodate deviations from standard cosmology and the Standard Model of particle physics.

In this paper, we prove energy and Morawetz estimates for solutions to the scalar wave equation in spacetimes with metrics that are perturbations, compatible with nonlinear applications, of Kerr metrics in the full subextremal range. Central to our approach is the proof of a global in time energy-Morawetz estimate conditional on a low frequency control of the solution using microlocal multipliers adapted to the $r$-foliation of the spacetime. This result constitutes a first step towards extending the current proof of Kerr stability in \cite{GCM1} \cite{GCM2} \cite{KS:Kerr} \cite{GKS} \cite{Shen}, valid in the slowly rotating case, to a complete resolution of the black hole stability conjecture, i.e., the statement that the Kerr family of spacetimes is nonlinearly stable for all subextremal angular momenta.

The detection of gravitational waves from binary black hole and neutron star mergers by ground-based interferometers, as well as the evidence for a gravitational wave background from pulsar timing array experiments, has marked a new era in astrophysics and cosmology. These experiments also have great potential for discovering new physics through gravitational wave detection. One of the most motivated sources of gravitational waves that can be realized only within a beyond-the-Standard-Model framework is first-order phase transitions. In this work we release PT2GWFinder, a Mathematica package designed to compute phase transition parameters and the gravitational wave power spectrum for an \textit{arbitrary scalar theory exhibiting a first-order phase transition, in scenarios where a single scalar acquires a vacuum expectation value. PT2GWFinder performs the phase tracing, computes the bounce profile and action using FindBounce, calculates the relevant temperatures and phase transition parameters, and finally evaluates the gravitational wave spectrum. Additionally, it offers a user-friendly interface with DRalgo, which enables the computation of the dimensionally reduced effective potential in the high-temperature regime. This work includes a user manual and two models that demonstrate the capability and performance of PT2GWFinder. As a supplement, for one of these models we obtain the bounce solution and action analytically in the thin-wall approximation and demonstrate excellent agreement with the numerical approach.

We present general relativistic magnetohydrodynamic simulations of binary neutron star (BNS) mergers, where the collapse of the metastable massive neutron star (MNS) remnant leads to the production of an incipient jet having terminal Lorentz factor and Poynting-flux luminosity compatible with a short gamma-ray burst (GRB). We consider different MNS lifetimes of about 25 and 50 ms, long enough for massive polar outflows to emerge before black hole (BH) formation. The interaction of the following BH-driven jet with such polar outflows, responsible for shock heating and possible electromagnetic signatures, is self-consistently captured for the first time. Exploiting an unprecedentedly low numerical density floor scaling as r^-6, we explore the jet propagation up to distances of ~10^4 km. Comparing the outcome of different MNS lifetimes, we find that the latter, by strongly affecting the propagation environment, plays a major role in determining the final properties of the escaping jet. Finally, we consider a non-collapsing case, where the MNS-driven outflow is found to exhibit a much higher density and lower velocity compared to the BH-driven jet.

We reveal a fundamental geometric structure of momentum space arising from the nonadiabatic evolution of Bloch electrons. By extending semiclassical wave packet theory to incorporate nonadiabatic effects, we introduce a momentum-space metric tensor -- the nonadiabatic metric. This metric gives rise to two velocity corrections, dubbed geometric and geodesic velocities, providing a unified and intuitive framework for understanding nonlinear and nonadiabatic transport phenomena beyond Berry phase effects. The geometric velocity is related to the nonadiabatic metric itself, whereas the geodesic velocity is a Christoffel symbol of the nonadiabatic metric. As the nonadiabatic metric is related to the energy-gap renormalized quantum metric, it unifies the broad quantum metric effects in electronic responses. When the nonadiabatic metric is constant, it reduces to an effective mass, modifying flat-band electron dynamics in confining potentials. In a flat Chern band with harmonic attractive interactions, the two-body wave functions mirror the Landau-level wave functions on a torus. Furthermore, we show that the nonadiabatic metric endows momentum space with a curved geometry, recasting wave packet dynamics as forced geodesic motion.

We show that superrotations can be described using the geometric conformal completion method of Penrose. In particular, superrotation charges can be described and calculated using the linkage method of Geroch and Winicour. Whether superrotation charges are calculated using the coordinate based Bondi formalism or the geometric Penrose formalism, the fact that the superrotation blows up at a point makes the superrotation charge formally ill defined. Nonetheless, we show that it can be made well defined through a regularization procedure devised by Flanagan and Nichols.

We investigate whether viscous cold dark matter (vCDM) in a $\Lambda$-dominated FLRW universe can alleviate the Hubble tension while satisfying thermodynamic constraints, examining both flat and curved geometries. We model vCDM with bulk viscosity $\zeta = \zeta_0\,(\Omega_{vc}/\Omega_{vc0})^m$, where $m$ determines the viscosity evolution and $\Omega_{vc}$ is the density parameter of vCDM. We explore two particular scenarios: constant viscosity ($m=0$), and variable viscosity ($m$ free). Using Bayesian inference, we constrain these models with the latest datasets: the Pantheon+ SN Ia sample (both with SH0ES calibration, PPS, and without it, PP), $H(z)$ measurements from CC and BAO as separate datasets, and a Gaussian prior on $H_0$ from 2022 SH0ES baseline, $H_0=73.04 \pm 1.04$ km/s/Mpc (R22 prior). We compare the models via information criteria such as AIC, BIC, DIC, and Bayesian evidence. Our results reveal that the Hubble tension persists, although it shows partial alleviation ($\sim 1\sigma$ tension) in all investigated scenarios when local measurements are included. For the flat $m=0$ case, the joint analysis yields $H_0 = 71.05^{+0.62}_{-0.60}$ km/s/Mpc. Curved model initially favors $\Omega_{K0} > 0$ (at more than $2\sigma$), but this preference shifts toward flatness once the PPS+R22 prior are included. Notably, the current viscosity is constrained to $\zeta_0 \sim 10^6$ Pa s in all scenarios, in agreement with the thermodynamic requirements. Although model selection via BIC and Bayesian evidence favors $\Lambda$CDM, AIC and DIC show mild support for viscous models in some datasets. Bulk viscous models moderately improve fits but neither resolve the Hubble tension nor outperform the $\Lambda$CDM model. To achieve more robust constraints, future analyses should incorporate CMB observations, which are expected to break parameter degeneracies involving $m$ and $\tilde{\zeta}_0$.

It is established that black holes have entropy and behave as thermodynamical systems. Associating entropy to gravitational fields has not remained limited to black holes, necessitating the notion of the second law of thermodynamics in gravitating systems. There have been many ideas and attempts to prove the second law in gravitational systems starting from first principles. Within the covariant phase space formalism, we define gravitational entropy as the charge associated with the local boosts, detaching the gravitational entropy from horizons or trapped surfaces. Our definition encompasses and generalizes the existing notions of entropy. Using this definition for the Einstein gravity case, we compute variations of the entropy along the path of any causal observer and establish that the entropy variations are always non-negative if the matter content satisfies the strong energy condition integrated along any segment of the causal path.

We consider the effective theory of heterotic strings in two spacetime dimensions, in a double field theory-inspired formalism, manifestly consistent with $T$-duality in string theory. Restricting the gauge group to a single $\mathrm{U}(1)$, we study the charged black hole solution and perform a precise analysis of the properties of the dual geometry with the $\mathrm{O}(1,2; \mathbb{R})$-valued generalized metric. We comment on some aspects related to singularities and gauge dependence. We show that the classification program for higher derivative corrections can also be applied to the heterotic case. We further elucidate how a previously proposed solution to the equations of motion, parametrized in a manner fully non-perturbative in $\alpha'$, can be extended to the scenario with $r$ abelian fields and the corresponding $\mathrm{O}(1,1+r; \mathbb{R})$ symmetry. We discuss some novel features of the solution for charged black holes.

The universal phase $\rev{\ii}^{D+2}$ of the Euclidean de Sitter path integral obstructs a straightforward state-counting interpretation of the Gibbons--Hawking entropy. Building on Maldacena's proposal that specific black-hole observers can reorganize this phase, we derive a general constraint on when such ``real observers'' can succeed. By distinguishing \emph{gravitational observers} from \emph{topological spectators}, we show at quadratic semiclassical order that any sector whose \emph{infrared effective} action is metric independent at the de Sitter saddle factorizes in the path integral, $\Ztot = \Zgrav^{(\text{obs})}\Ztop$, so the imaginary phase persists regardless of the sector's information-processing capabilities. Using confining $\SU(3)$ gauge theory and topological orders as examples, we demonstrate that an information-bearing clock is necessary but insufficient: only observers whose fluctuations share the negative modes of the conformal factor belong to the special class that can remove the de Sitter phase.

Extreme mass-ratio inspirals (EMRIs), comprising a stellar-mass compact object (CO) orbiting a supermassive black hole (BH), are key targets for future space-based gravitational-wave (GW) observatories. Incorporating the spin of the secondary body into waveform models not only enhances measurement precision but also offers insight into the spin distribution of stellar-mass objects. In this work, we construct the flux and waveform for an EMRI with a spinning secondary in a Kerr background under the linear-spin approximation. Using the radiative prescription (half-retarded minus half-advanced field), we derive orbit-averaged evolution equations for the fundamental constants of motion, including the energy, angular momentum, Carter-like constant, and the parallel spin component. This framework provides a tractable route to generating waveforms that incorporate the secondary spin, with the potential for further simplification in future work.

We investigate the potential to detect low-frequency gravitational waves (GWs) through their imprints on the proper motions of distant quasars observed by the Gaia mission. Using astrometric data from Gaia DR3, we simulate the effect of GWs on the proper motions of quasars, incorporating their actual sky positions and measurement uncertainties. We investigate two data analysis techniques for the extraction and characterization of GW signals from quasar proper motions: Vector Spherical Harmonics (VSH) and angular correlation functions, commonly referred to as Hellings-Downs curves (HDC). Using realistic simulated data, we forecast their sensitivity and accuracy to GWs, and evaluate the impact of systematic errors. From these simulations, we derive an upper limit on the amplitude of a stochastic GW background, constrained by the observational timespan, astrometric precision, and the sky distribution of quasars. Compared to HDC, VSH appears more statistically robust, less prone to selection effects, and with a significantly smaller computational cost, scaling as N. The HDC method is more sensitive for detecting gravitational waves, but its complexity scales as N^2. We find that, with Gaia DR3 proper motion errors, the lower limit for a detectable GW strain is of 10^{-11}, with possible improvements to about 3 x 10^{-12} for the next Gaia Data Release 4 (for the same number of quasars). This limit holds for a stochastic GW spectrum integrated over all frequencies less than half the inverse of the 34-month observational timespan of Gaia DR3, corresponding to approximately 5.6 nHz. We also investigate how different data-restriction and weighting schemes influence the final estimate of the gravitational wave strain.