In this work, we investigate the thermodynamics and motion of neutral test particles around a regular black hole immersed in a perfect fluid dark matter environment. We begin by examining the horizon structure and key thermodynamic properties, with particular emphasis on quantities such as the Hawking temperature and the specific heat capacity. These aspects provide important insight into the stability and physical behavior of the black hole system. We then proceed to analyze the dynamics of neutral test particles using the Hamiltonian formalism, through which we derive the effective potential governing particle motion. Using the effective potential, we further study quasiperiodic oscillations by determining the associated epicyclic frequencies and comparing them with available observational data. Using the observed QPO data of XTE J1550-564, GRO J1655-40, GRS 1915+105, and M82 X-1, we perform a Markov Chain Monte Carlo analysis to constrain the black hole mass, the magnetic charge parameter, the PFDM parameter, and the characteristic orbital radius. Finally, we investigate the black hole shadow and demonstrate how various geometric parameters influence its optical appearance. This analysis highlights the potential observational signatures of such black holes and their surrounding dark matter environment.

We focus our attention on the spinor model proposed in an article by J. Magueijo et al. and we analyze it from the point of view of the cosmological background. We show that this model, under some conditions, can well-describe the background behavior of DM and, under other conditions, the behavior of DE. Furthermore, we show that the SET of the spinorial fluid, in the context of the cosmological background, can be recast in the form of that of a Perfect Fluid whose four-velocity is given by the normalized vector current density. Successively, we concentrate on the analysis of the scalar cosmological perturbations of this model, following the usual SVT Decomposition approach. We show that the treatment of cosmological perturbations is very difficult and cannot be done directly. Due to this fact, we tackle the problem with another method: the (1+3)-decomposition. We prove that we can further decompose the SET of a spinorial fluid, thanks to the presence of the axial current density. Employing the results found in an article by L. Fabbri et al. and the polar form of spinors, we show how the thermodynamical quantities that characterize the spinorial fluid can be written in terms of the four-velocity, the normalized axial current density, the chiral angle, and the projector on the hyperplane orthogonal to the first two. Moreover, in the context of scalar perturbations, we obtain an expression for the adiabatic speed of sound of the pressure perturbation in terms of the parameters that characterize the spinorial field written in polar form. In the end, we tackle the problem of spherically symmetric halos surrounding galaxies by analyzing the behavior of the SET of the spinorial fluid in a spherically symmetric space-time. We prove that, in general, none of its components vanish, giving rise to the problem of the suitability of the model for the description of spherically symmetric objects.

We explore the properties of bilinear products for black-hole quasinormal modes (QNMs) formulated on hyperboloidal foliations. We find that, although QNM solutions are smooth and finite on future-directed hyperboloids, the integrand of the bilinear form with respect to which the modes are orthogonal is still divergent. This is a result of the reflection (equivalently, CPT) transformation required in the definition of the products, which modifies the behaviour of the integrand at the boundaries. We present several regularisation procedures that yield a finite and well-defined bilinear form. In addition, we examine an alternative definition of the bilinear products that incorporates flux contributions, discussing its advantages and limitations. Finally, we define the QNM excitation factors and coefficients within the hyperboloidal framework in terms of the bilinear products, and compute them explicitly for a choice of mode numbers and constant initial data. For concreteness, we work with the QNMs associated to scalar perturbations of the Schwarzschild family of spacetimes.

We demonstrate the uniqueness of the spacetimes recently found by us in [H. Ovcharenko and J. Podolsky, Phys. Rev. D 112 (2025) 064076]. First, we prove that the conformal-to-Carter metric ansatz we used therein is the only possible for stationary axisymmetric geometries that are of Weyl type D, with geodesic and shear-free principal null directions (PNDs) which are orthogonal to polar directions, and whose specific 1-form $\theta$ is closed. Because this result is general, without employing any field equations, such conformal-to-Carter metric may find interesting applications also in various alternative theories of gravity. Then, we show that in the Einstein-Maxwell theory the only non-trivial electrovacuum solution for the conformal-to-Carter metric with the fully non-aligned and non-null electromagnetic field is the Ovcharenko-Podolsky class found in 2025. Complementarily, the only solution with the double-aligned and non-null electromagnetic field is the Plebański-Demiański class found in 1976.

The oscillation modes of stars play an important role in observations, and on the understanding of stellar stability properties. The role of viscosity in the oscillation modes of compact stars has been so far understood very loosely only, in absence of a well posed framework. We use recent breakthroughs in the formulation of a causal and stable theory of relativistic hydrodynamics, to study oscillation modes of neutron stars. We characterize the axial spectrum of compact stars and uncover new, viscosity-driven families of modes, without a perfect fluid counterpart. Our results show mode avoidance in some of these families, and a spectrum of long-lived modes, whose role in astrophysical, dynamical processes is yet to be understood.

In this paper, we study the gravitational lensing around the static and spherically symmetric DD black holes, which we recently derived as perturbations of the Schwarzschild geometry within the revised Deser-Woodard theory of nonlocal gravity. We first present general analytical expressions for the deflection angle in both weak- and strong-deflection limits, explicitly relating them to the nonlocal corrections to Schwarzschild spacetime. Subsequently, we analyze lensing observables, such as the post-Newtonian effects and the black hole shadow, to constrain the DD black hole parameter space using current observational bounds. Finally, we perform a joint statistical analysis based on the Fisher information matrix, combining these findings with our previously obtained constraints from quasinormal modes. Our results indicate consistency with general relativity at the $1.13\sigma$ level. This work provides a first assessment of the DD parameter space and offers new insights to probe deviations from Einstein's gravity in view of future larger datasets.

We consider a hybrid metric-Palatini theory whose action depends on the metric and Palatini scalar curvatures, together with the corresponding quadratic Ricci invariants, through an arbitrary function $f(R,\mathcal{R},\mathcal{R}_{\mu\nu}R^{\mu\nu},R_{\mu\nu}R^{\mu\nu},\mathcal{R}_{(\mu\nu)}\mathcal{R}^{(\mu\nu)})$. We derive the associated field equations and linearize them around Minkowski spacetime in order to analyze the dynamical content of the theory. This formulation allows us to compute the graviton propagator and to identify the additional spin-2 and spin-0 modes generated by the mixed metric-affine structure. We show that, in general, the Ricci-squared terms give rise to a massive spin-2 ghost, and we determine the algebraic conditions on the background derivatives of $f$ required to eliminate it, leaving only healthy scalar excitations. Several relevant subclasses -- including hybrid $f(R,\mathcal{R})$, $f(\mathcal{R},\mathcal{R}_{(\mu\nu)}\mathcal{R}^{(\mu\nu)})$, $f(R,\mathcal{R}_{(\mu\nu)}\mathcal{R}^{(\mu\nu)})$, and the purely metric $f(R)$ and Palatini $f(\mathcal{R})$ cases -- are recovered as limiting regimes, and their ghost- and tachyon-free conditions are obtained in a unified way. Altogether, this establishes a systematic framework for assessing the theoretical consistency of extended hybrid metric-Palatini gravity theories.

We present a novel class of rotating dilatonic solutions within the framework of Einstein-ModMax-type gravity. The configuration belongs to the nonlinear sector characterized by $\mathcal F/\mathcal G=\mathrm{const}$ and carries nontrivial electric and magnetic potentials, with both $A_t$ and $A_\varphi$ turned on, together with a nontrivial gravitomagnetic structure. We show that this solution does not admit continuation to the Maxwell framework of our parametrization, so it is intrinsically tied to the nonlinear ModMax regime. It includes both a NUT geometry and a NUT-free asymptotically flat limit, and it is valid for a broad class of dilatonic couplings, including the low-energy string and Kaluza-Klein cases. Moreover, in the prolate sector we identify a genuine black-hole regime in which the exterior region satisfies the null energy condition while the curvature singularity remains hidden behind the event horizon. These results provide an exact rotating dilatonic ModMax configuration with no Maxwell analog and a physically well-behaved exterior black-hole sector.

The Event Horizon Telescope (EHT) has guided strong-field gravitational physics by providing the first direct images of the supermassive black holes M87* and Sagittarius A*. The EHT observations offer unprecedented opportunities to test modified gravity theories against general relativity (GR). Motivated by this, we investigate charged rotating black holes in KR gravity, a framework motivated by string theory that incorporates spontaneous Lorentz symmetry breaking. The spacetime geometry is characterized by a Lorentz--violating parameter $\ell$ and electric charge $Q$, which modify the Kerr--Newman metric through a radial-dependent mass function. We compute black hole shadows and derive constraints on $\ell$ and $Q$ using EHT observations of M87* and Sgr A*. For angular shadow diameter $\theta_{\rm sh}$ of M87* at inclination $\theta_o=17^\circ$ and fixed $Q=0.2$, the EHT-allowed range $\theta_{\rm sh}\in(35.1,\,40.5)\,\mu\mathrm{as}$ constrains the Lorentz--violating parameter to approximately $-0.019\lesssim\ell\lesssim0.075$ and $-0.076\lesssim\ell\lesssim0.029$ across the admissible spin interval. For angular shadow diameter $\theta_{\rm sh}$ of Sgr A* at inclination $\theta_o=50^\circ$ and fixed $Q=0.2$, the corresponding EHT-allowed range $\theta_{\rm sh}\in(41.7,\,55.7)\,\mu\mathrm{as}$ permits approximately $-0.075\lesssim\ell\lesssim0.110$ and $-0.124\lesssim\ell\lesssim0.076$ across the admissible spin interval. Our analysis reveals that the Lorentz-violating parameter suppresses the shadow radius by a factor $\sqrt{1-\ell}$, while charge introduces additional distortions. Using the angular shadow diameter measured by EHT, we obtain an upper bound $\ell \lesssim 0.19$ from Sgr A* data with the stellar dynamics mass prior.

We compute the quasinormal mode spectrum of scalar perturbations on Kaigorodov pp-wave spacetimes, the horizonless gravity duals of zero temperature null fluids. The pp-wave deformation promotes the Poincaré horizon at $r=0$ to an irregular singular point of rank $(d+2)/2$, which acts as a geometric absorber for ingoing waves: rank~$0$ corresponds to thermal dissipation, rank~$1$ to quantum-critical (extremal black hole), and rank~$\geq 2$ to gapped, horizonless dissipation. For $d=2$ (extremal BTZ) the radial equation reduces to the Whittaker equation with exact non-dissipative spectrum $\mathrm{Im}(\omega)=0$; for $d \geq 3$ all modes satisfy $\mathrm{Im}(\omega_n) < 0$, establishing zero temperature dissipation without horizon or entropy. At zeroth order the radial equation becomes Bessel's equation of order $\mu=d/(d+2)$, proving all scalar QNMs are gapped. Numerical spectra for $d=3,4,5$ yield a discrete dissipative tower and confirm linear stability.

Multiple potential wells for massive test particles, allowing distinct families of bound orbits to coexist, are a characteristic feature of certain exotic compact objects beyond general relativity. Taking the dyonic black hole as a representative example, we demonstrate that such multi-well geometries generically support multiple coexisting branches of bound orbits, in contrast to the single-branch behavior observed in the Schwarzschild spacetime. Crucially, the periodic orbits sharing identical rational rotation number, and hence identical topological indices can nevertheless produce \emph{radiatively distinct} gravitational waves in a representative extreme-mass-ratio inspirals: their amplitude modulation and harmonic content differ because each branch spans different regions of spacetime curvature. These ``topologically equivalent yet waveform-distinguishable'' signatures provide a direct observational probe of strong field gravitational dynamics beyond general relativity, potentially accessible to future space-based gravitational wave detectors.

The addition of KAGRA to the global gravitational-wave detector network introduces new baselines and complementary antenna response patterns that can enhance sky localization for compact binary coalescences. We investigate KAGRA's role in the LIGO-Virgo-KAGRA network using a systematic injection study of binary neutron star signals. Sky maps are constructed with a radiometric, coherence-based framework, allowing isolation of geometric and timing contributions from individual detectors. Localization performance is quantified using the fraction of events localized within $100~\mathrm{deg}^2$, cumulative area distributions, and the median $90%$ credible region. We also assess KAGRA's impact on detection rates by varying its sensitivity over a wide range. Even at its current sensitivity of $\sim10~\mathrm{Mpc}$, KAGRA provides measurable improvements by breaking degeneracies through additional baselines and directional constraints. As sensitivity increases, improvements in signal-to-noise ratio and timing precision lead to substantial reductions in localization area. We identify a binary neutron star range of $\sim30~\mathrm{Mpc}$ as a practical benchmark for reliable localization suitable for electromagnetic follow-up, noting this as a conservative estimate. In addition, KAGRA increases the number of detectable events by enabling lower signal-to-noise detections. These results demonstrate that even a modest-sensitivity detector can significantly enhance network performance through geometric complementarity, highlighting the importance of a geographically distributed network for multimessenger gravitational-wave astronomy.

We develop an analytic eikonal description of perturbations for four-dimensional regular black holes in quasi-topological gravity. Using first-order Schutz--Will WKB together with a small-coupling expansion and a large-$\ell$ expansion, we obtain closed quasinormal-mode formulas with explicit dependence on the black-hole parameters $(M,\mu,\nu,\alpha)$. We then map the same geodesic invariants $(\Omega_{\text{ph}},\lambda_{\text{ph}})$ to shadow and strong-lensing observables, deriving an explicit QNM--shadow--lensing correspondence. In this way, ringdown frequencies, shadow scale, and strong-deflection observables are unified in one analytic scheme for this quasi-topological family.

We study spontaneous scalarization of a scalar field in the magnetized Reissner--Nordström spacetime induced by parity-violating and parity-preserving interactions, represented by couplings to the electromagnetic Chern--Simons, gravitational Chern--Simons, and Gauss--Bonnet invariants, respectively. Working in the decoupling limit, we evolve scalar perturbations in the time domain and determine the critical coupling for the onset of tachyonic instability. This allows us to compare, within the same magnetized background, how the external magnetic field affects scalarization induced by parity-violating and parity-preserving interactions. We find that the magnetic field lowers the scalarization threshold in the electromagnetic and gravitational Chern--Simons channels. In the Gauss--Bonnet channel, by contrast, the effect divided into two branches: on the negative-$\alpha$ branch in our convention, corresponding to the standard GB$^{+}$ branch, the magnitude of the critical coupling increases with the magnetic field, whereas on the positive-$\alpha$ branch, corresponding to GB$^{-}$, the critical coupling decreases with the magnetic field but diverges in the limit of vanishing field. The magnetic field also modifies the late-time dynamics and gives rise to Melvin-like modes. When nonlinear couplings are included, the unbounded growth of the linearized theory is replaced by bounded oscillatory evolution. These results show that external magnetic fields affect scalarization induced by parity-violating and parity-preserving interactions in qualitatively different ways, and reveal a pronounced asymmetry between the two Gauss--Bonnet branches.

We investigate the consistency and precision of approximate analytical expressions for the electromagnetic self-force acting on a charged particle in Schwarzschild spacetime endowed with weak electromagnetic fields. A fundamental requirement of relativistic particle dynamics is the preservation of the four-velocity normalization ($u^\mu u_\mu=-1$), which implies that the total self-force must remain orthogonal to the particle's four-velocity. We introduce a covariant diagnostic based on the orthogonality condition ($u_\mu F^\mu_{\text{tail}}=0$), which provides a quantitative measure of the internal consistency of approximate tail-term models used in radiation-reaction calculations. We apply this diagnostic to two widely used analytical approximations for the electromagnetic tail force: the conservative component derived by Smith and Will and the dissipative component derived by Gal'tsov. The analysis is performed for several physical configurations, including pure Schwarzschild spacetime, a weakly electrically charged Schwarzschild black hole, and a Schwarzschild black hole immersed in a weak external magnetic field. We find that the conservative Smith--Will term alone leads to small but measurable deviations from the orthogonality condition, while inclusion of the dissipative Gal'tsov contribution suppresses these deviations by many orders of magnitude. For realistic radiation-reaction parameters, the violation becomes extremely small. The proposed orthogonality diagnostic offers a simple and covariant tool for validating approximate self-force models in curved spacetime and may be useful for future studies of radiation-reaction dynamics near compact objects.

Glitches frequently contaminate data in gravitational-wave detectors, complicating the observation and analysis of astrophysical signals. This work introduces VIGILant, an automatic pipeline for classification and visualization of glitches in the Virgo detector. Using a curated dataset of Virgo O3b glitches, two machine learning approaches are evaluated: tree-based models (Decision Tree, Random Forest and XGBoost) using structured Omicron parameters, and Convolutional Neural Networks (ResNet) trained on spectrogram images. While tree-based models offer higher interpretability and fast training, the ResNet34 model achieved superior performance, reaching a F1 score of 0.9772 and accuracy of 0.9833 in the testing set, with inference times of tens of milliseconds per glitch. The pipeline has been deployed for daily operation at the Virgo site since observing run O4c, providing the Virgo collaboration with an interactive dashboard to monitor glitch populations and detector behavior. This allows to identify low-confidence predictions, highlighting glitches requiring further attention.

We extend the investigation into the formation of shell-crossing singularites (SCS) in effective polymerized LTB models to the LQG-inspired asymmetric bounce model, as well as to effective LTB models based on the solutions of Bardeen and Hayward, in which no bounce occurs. While the asymmetric bouncing model belongs to the class of bounded polymerization functions, the latter models feature unbounded polymerization functions. Our results show that, similar to the symmetric bouncing model, for the asymmetric bouncing model SCS are unavoidable for inhomogeneous dust profiles. In contrast, for models without a bounce and with unbounded polymerization functions, no SCS form for inhomogeneous, decreasing dust profiles -- a situation that resembles classical theory, in which SCS can also be avoided by a suitable choice of initial data.

Timelike orbits in curved spacetimes encode intrinsic information about the background geometry and serve as critical probes for investigating gravitational theories and source distributions. In this study, we investigate strictly closed timelike orbits within a Schwarzschild spacetime embedded in a Dehnen-type dark matter halo. By solving the geodesic equations, we identify various configurations of these closed orbits and simulate their corresponding gravitational waves and electromagnetic light curves. Our findings reveal that the morphology of closed orbits is primarily governed by the ratio of the azimuthal period to the radial period. Notably, dark matter halo parameters such as the core scale and density parameters exert a significant amplification effect on the orbital scale, which further induces a discernible phase lag in the gravitational wave signals. Furthermore, although certain orbital structures including the number of leaves remain challenging to distinguish via gravitational wave signals alone, they exhibit identifiable signatures in the characteristic peaks of light curves. These findings reveal the multi-messenger potential of closed orbits in bridging black hole environments and dark matter properties, providing theoretical guidance for future dark matter searches.

We present Basilic, a dedicated pipeline for Bayesian model selection and parameter estimation of short-duration gravitational-wave burst signals observable with ground-based detectors. Built on top of the bilby framework, Basilic combines modularity, pre-implemented burst models, and HTCondor integration to enable rapid, user-friendly analyses with minimal technical overhead. This work outlines the design philosophy, operational flow, and a set of example use cases demonstrating its scientific potential. As a case study, we also undertake an in-depth exploration of the comparison between a binary black hole merger and a cosmic string signal, through a parameter space exploration injection campaign. In addition to the well-known high-mass binary black-hole signal morphology degeneracy with cosmic string-like signals, we find that high anti-aligned component spins, even at moderate mass, can result in a similar degeneracy. Motivated by the likely low-SNR expected regime of possible future detections, we propose a data-driven study of model degeneracy, to be employed in the event of an inconclusive Bayes factor.

Transient noise artifacts, commonly referred to as glitches, pose a major challenge to parameter inference for space-based gravitational-wave (GW) observations. We develop a glitch-robust amortized inference framework for massive black hole binaries in the Taiji detector configuration by combining conditional normalizing flows, a time-frequency multimodal fusion encoder, and contrastive learning. To enable large-scale training on contaminated data, we further introduce a neural glitch generator that produces high-fidelity synthetic transients at substantially reduced computational cost. Systematic experiments show that, under glitch contamination, the proposed method yields more accurate and better-calibrated posteriors than a conventional Markov Chain Monte Carlo baseline. In ablation studies, the full time-frequency model with contrastive learning performs best overall and remains robust to variations in glitch duration and merger-relative timing. We further show that standard coverage diagnostics alone are insufficient to fully assess posterior fidelity. We therefore complement them with the continuous ranked probability score, which provides a stricter assessment of global distributional agreement in non-ideal GW data. Taken together, these results establish deep-learning-based amortized inference as a promising framework for fast and robust Bayesian parameter estimation in future space-based GW observations.

In this article, we revisit the thermodynamics of Hayward black holes [1] in asymptotic flat spacetime and obtain the bounds on the final mass post merger after head-on collision event of two equal mass black holes. We revisit thermal properties of these black holes from a perspective that the laws of black hole thermodynamics remain valid. Under this condition a novel entropy formula appears naturally with a logarithmic correction term along with one extra term. We discuss phase structure of the black holes. Next, we obtain the bounds on the final black hole mass parameter using the validity of the second law of black hole thermodynamics with the new entropy formula. We discuss the impact of the Hayward parameter on thermal and merger properties of these black holes.

We study the Tolman-Oppenheimer-Volkoff equation in the presence of a cosmological constant for general thermodynamically consistent equations of state, without imposing regularity at the center. Formulating the problem as an initial value system integrated from an outer boundary inwards, we obtain a general classification of solutions and show that singular configurations dominate the solution space. We demonstrate that all singular solutions share a universal geometric structure and give rise to spacetimes that are bounded-acceleration complete, indicating that the associated singularities are comparatively mild. Our results extend the classification previously obtained for {\Lambda}=0 and reveal qualitatively new features for $\Lambda \neq 0$. For $\Lambda < 0$, we identify solutions with approximate horizon structures that mimic black holes in equilibrium with their Hawking radiation. For $\Lambda > 0$, we find four distinct classes of solutions with cosmological horizons, distinguished by the behavior of their temperature gradients.

We explore hidden symmetries in electrically charged, four-dimensional rotating Kerr-Newman black hole within $f(R)$ gravity. By deriving the Killing and Killing-Yano tensors, we establish their role in the spacetime structure. The gyromagnetic ratio is calculated and shown to retain its universal value of $g = 2$, consistent with all four-dimensional black holes. These findings show that the gyromagnetic ratio remains consistent in this modified gravity setting. Moreover, they highlight the connection between hidden symmetries and the ability to separate the Hamilton-Jacobi equation in $f(R)$ gravity. This work advances the study of black holes in modified gravity, offering implications for both theoretical frameworks and observational cosmology, such as gravitational wave analyses.

We study physical (near-kernel of constraints) states of 4-d Euclidean loop quantum gravity in Smolin's weak coupling limit on the complete graph $K_5$ using variational Monte Carlo with neural network quantum states. We investigate the Hamilton constraint $\hat{H}$ in the ordering proposed by Thiemann, as well as $\hat{H}^\dagger$ and $\hat{H}+\hat{H}^\dagger$. We find that the variational optimisation selects distinct solution families for $\hat{H}$ and $\hat{H}^\dagger$ across several considered cutoffs on the kinematical degrees of freedom. The solution family of $\hat{H}$ is flat on all minimal loops and has non-vanishing volume expectation values. Its edge-charge marginals delocalise with increasing cutoff, which indicates they are approximations to solutions that are non-normalisable in the kinematical inner product. The solution family for $\hat{H}^\dagger$ is normalisable, shows non-trivial charge correlations, lies in the kernel of volume and is not flat. $\hat{H}+\hat{H}^\dagger$ turns out to be much harder to solve and yields quasi-solutions combining features of both previous families. We characterise all solutions using chromaticity 1- and 2-point functions, minimal loop holonomies, geometric area and volume observables and show that the two families can be interpreted as, on the one hand, a family of states close to the Ashtekar-Lewandowski vacuum and the Dittrich-Geiller vacuum with some numerical noise on the other hand. We also present some results that link solutions of the truncated theory to solutions of the continuum theory.

Black hole shadow images are primarily determined by the properties of photon spheres and can exhibit degeneracies across different spherically symmetric spacetime geometries. We show that time delay observables associated with higher-order images of transient sources provide a robust probe to break such degeneracies in spacetimes admitting multiple photon spheres. Adopting a model-independent, parametrized, static, spherically symmetric framework that captures the generic features of double-peaked effective potentials, we investigate photon geodesics and quantify them in terms of angular deflection, travel time, and the order of the image. We identify distinctive signatures of trajectories probing the region between the unstable photon spheres. In particular, we find that these trajectories are characterized by the nontrivial temporal behavior, including a minimum travel time, a minimum angular deflection, and a characteristic triplet structure of higher-order images with a specific arrival sequence. We further show that the influence of the depth of the potential well, between the two photon spheres, on the observed time delays provides a direct handle on otherwise inaccessible regions of the spacetime. Our results highlight that time-domain lensing observables encode information beyond static shadow images and offer a promising avenue for probing the structure of compact objects and the strong-field regime of gravity.

We introduce a cyclotomic representation for finite $q$-hypergeometric series and $q$-deformed amplitudes that separates algebraic structure from evaluation. By expressing each summand in a sparse exponent basis over irreducible cyclotomic polynomials, all products and ratios of quantum factorials reduce to integer vector arithmetic. This ensures that cancellations between numerator and denominator are resolved exactly prior to any evaluation. This formulation yields the deferred cyclotomic representation (DCR), a parameter-independent combinatorial object of the series, from which evaluation in any target field is realized as a ring homomorphism. For quantum recoupling coefficients, we demonstrate that this framework achieves linear memory scaling in the compilation phase, eliminates intermediate expression swell in exact arithmetic, and substantially extends the range of reliable double-precision computation by reducing cancellation-induced error amplification. Beyond its computational advantages, the DCR provides a unified perspective on $q$-deformed amplitudes. Structural properties like admissibility at roots of unity, and the classical limit all emerge as intrinsic properties of a single underlying combinatorial object.

We extend Penrose's quasi-local mass definition to include higher-spin charges associated with the celestial $Lw_{1+\infty}$ symmetries and relate them to traditional definitions of multipoles. The resulting formulae provide explicit expressions that can be computed on finite 2-surfaces, given a choice of null hypersurface. They yield a geometric definition of celestial symmetries and multipoles in generic spacetimes in terms of higher-valence solutions to the twistor equations. This, in turn, gives rise to natural flux-balance laws along the null hypersurface. We also present a first-principles phase-space derivation of these charges, starting from a twistor space action for self-dual gravity that can be identified with the standard gravitational asymptotic phase space at null infinity, performing a large gauge transformation analysis and using the Penrose transform to connect with the corresponding spacetime expressions. Finally, we formulate the spacetime analysis in the Plebanski gauge and relate the celestial symmetries to the integrability of self-dual gravity in the case of a self-dual background.

We show that the strong constraints placed by Planck NPIPE Cosmic Microwave Background (CMB) data on axion-like early dark energy (EDE) are significantly alleviated in models with multiple fields. We find a $1.5\sigma$ residual tension with the Local Distance Network value of $H_0$ in a 2-field model, with no improvement beyond two fields, and a best-fit value of $H_0$ $\sim 1.4\sigma$ larger than in the 1-field case. The second field improves the fit to high-$\ell$ CMB data, where 1-field EDE is most strongly disfavored, and suggests modifications to the pre-recombination history over a wider redshift range.

[Abridged] A variety of model-dependent as well as model-independent approaches suggest that certain localized features in the primordial scalar power spectrum can lead to a significantly better fit to the observed anisotropies in the cosmic microwave background (CMB). In this work, we focus on three types of such features and examine whether these features can be generated in inflationary scenarios driven by a single, canonical scalar field. We consider a slowly rolling baseline model that is described by a specific time-dependence of the first slow roll parameter and we generate the desired features in the power spectrum through suitable modifications to the functional form of the slow roll parameter. To systematically reconstruct the desired features in the scalar power spectrum (or, equivalently, the modifications in the behavior of the first slow roll parameter) that are consistent with the data, we implement a machine learning pipeline based on the genetic algorithm (GA). Assuming the standard values for the background $\Lambda$CDM model (arrived at for a nearly scale-invariant primordial scalar power spectrum), we apply our method to the Planck 2018 CMB data, and show that the reconstructed features improve the fit to the observed angular power spectra by $\Delta \chi^2 \lesssim -10$. Moreover, we find that GA points to other sets of background parameters and primordial features, which lead to a similar level of improvement in the fit to the data. Such alternative sets of background parameters and scalar power spectra offer possible pathways to alleviate existing cosmological tensions. Our approach provides effective single-field inflationary dynamics to generate features that are supported by the data.

We derive a one-loop effective description of axion inflation by integrating out a heavy Dirac fermion with an inflaton-dependent complex mass undergoing a smooth localized threshold transition. The threshold induces correlated corrections to the inflaton and gauge sectors, including a Coleman-Weinberg term, a vacuum-polarization correction, and an anomaly-induced Chern-Simons coupling. Together, these effects transiently enhance and localize gauge-field production, generating a chiral stochastic gravitational-wave background in the deci-hertz band within the projected sensitivities of BBO and DECIGO, while remaining below representative primordial-black-hole bounds.

Early observations from the James Webb Space Telescope (JWST) have revealed an overabundance of massive high-redshift galaxies, raising the question of whether this points to new physics beyond $\Lambda$CDM, or an enhanced formation efficiency of massive stars. We revisit this issue going beyond earlier analyses based on direct comparisons to theoretical bounds at a fixed cosmology, by performing a full Bayesian analysis of the most extreme galaxies in the CEERS imaging and FRESCO spectroscopic samples, jointly constraining cosmological parameters and the baryon-to-star conversion efficiency $\epsilon$. We do so not only within the spatially flat $\Lambda$CDM model, but also in models where the dark energy equation of state $w$ and/or the spatial curvature parameter $\Omega_K$ are allowed to vary, carefully discussing the impact of both $w$ and $\Omega_K$ on the cumulative comoving stellar mass density. Within the flat $\Lambda$CDM model, once cosmological parameters are marginalized over, the CEERS sample provides a weak $2\sigma$ lower limit of $\epsilon \gtrsim 0.07$, compatible with astrophysical expectations. In contrast, the FRESCO sample requires $\epsilon \gtrsim 0.5$ at $2\sigma$, with values $\epsilon \lesssim 0.2$ disfavored at $>5\sigma$. These results do not qualitatively change when we allow $w$ and/or $\Omega_K$ to vary, with no evidence for deviations from $w=-1$ or $\Omega_K=0$. Our results therefore suggest that the origin of the ``JWST tension'' is unlikely to be cosmological, but lies in the astrophysics of galaxy formation.

We study bipartite entanglement harvesting from the quantum vacuum of a massless scalar field between two subsystems, each composed of a finite number of Unruh-DeWitt detectors. Using perturbation theory, we show that the leading-order negativity is fully determined by a submatrix of the reduced density matrix, with the submatrix dimension scaling only linearly with the number of detectors. Within this framework, we analyze how the detectors' spatial arrangement influences harvesting. For all three-detector configurations and several symmetric four-detector configurations, we derive analytic expressions for the negativity and identify the configurations that maximize it. For a linear chain, we find that the harvested entanglement scales linearly with the number of detectors. These results clarify how to arrange multiple detectors to optimize harvesting and show that increasing their number broadens the ranges of energy gaps and separations over which entanglement can be extracted from the field.

The KM3NeT Collaboration reported the detection of a neutrino, designated as KM3-230213A, with a reconstructed energy peaking at 220 PeV and equatorial coordinates (J2000) of RA=$94.3\degree$ and Dec=$-7.8\degree$. As the highest-energy neutrino event documented to date, its astrophysical origin remains unascertained. Prior preliminary investigations have probed potential associations between this neutrino event and gamma-ray bursts (GRBs), factoring in the possibility of Lorentz invariance violation (LV). In this study, we perform a comprehensive analysis to explore correlations between KM3-230213A and all viable GRBs. We explicitly account for the angular uncertainties intrinsic to both the neutrino event and the respective GRBs. Our analysis identifies a larger set of correlated GRBs. For each associated GRB, we compute the LV scale, integrating uncertainties from redshift measurements and neutrino energy determinations to enhance the robustness of our findings.

The mean value of the stress-energy tensor of a given quantum field theory at global thermodynamic equilibrium in a curved space-time can be expressed in terms of the derivatives of the Killing four-temperature field and the derivatives of the metric tensor. Its asymptotic expansion about zero includes an analytic part made of integer powers of these derivatives - corresponding to the so-called gradient expansion - as well as non-perturbative corrections. By using available exact solutions for the free real massless scalar field, we show that in the case of Minkowski, de Sitter, anti-de Sitter, and closed Einstein universe, the analytic part - obtained through the procedure of analytic distillation - has a finite number of terms and it is the same once expressed in a covariant form. On the other hand, non-universal terms are non-analytic in these derivatives and correspond to boundary conditions or to specific global properties of the space-time. We argue that the universality of the analytic part extends to any quantum field theory on a curved background.

The performance of mirrors in optical interferometers is critically influenced by their surface quality. Accurate metrology enables mirror surfaces to be characterized through phase maps describing their three-dimensional structure after coating. In this work, we combine Zernike polynomial decomposition and spatial frequency (PSD) analysis with numerical optical simulations to quantify the impact of surface distortions on the reflected optical field. The method is validated using metrology data from mirrors currently installed in the Advanced Virgo gravitational-wave detector. Building on this validation, we introduce a framework for generating realistic virtual mirror maps that reproduce both low order aberrations and high spatial frequency content of measured surfaces. These virtual maps are used in optical simulations to systematically explore and compare candidate surface quality specifications for future detectors, with particular focus on the Einstein Telescope. Our results show that metrology-informed virtual mirrors provide a practical design tool to assess the impact of different surface specifications on optical performance, and to relate future requirements to the performance of existing interferometers.

We investigate the properties of charged black hole geometries in nonlinear electrodynamics. We focus on the recently reported analytic charged black hole solutions to illustrate the consequences of a non-monotonic lapse function that exists for a wide range of black hole solutions. The spacetime admits stable light-rings, static near-horizon observers, and trapped near horizon photon orbits. We also show that although these modifications near the horizon are screened from afar, they nonetheless lead to additional branches of quasinormal modes for the black hole that are longer lived than the canonical Einstein branches.

Within the wide variety of topological solitons supported by Yang--Mills theory, merons occupy a particularly distinguished role. Despite their simplicity, they represent genuinely non-Abelian configurations that can be regarded as the fundamental building blocks of instantons, and they provide a qualitatively accurate picture of confinement. In this work, we show that such configurations are, in fact, supported by a broad class of non-Abelian gauge theories beyond Yang--Mills, provided that suitable physical conditions are satisfied, thereby rendering them universal. Taking into account their gravitational backreaction, we further demonstrate that both black holes and Euclidean wormholes sourced by merons admit natural extensions within this generalized framework, which regularizes the singular behavior they exhibit in constant--curvature backgrounds. As a byproduct, we construct a regular black hole solution supported by genuinely non-Abelian gauge fields, based on a non-Abelian generalization of the Ayón--Beato--García nonlinear electrodynamics. As a consequence of this universality, physical effects intrinsic to merons are likewise expected to be universal. A notable example is the spin from isospin effect, whereby bosonic excitations charged under the gauge group can effectively behave as fermionic degrees of freedom.

In the effective field theory (EFT) description of binary inspirals, the radiated gravitational waveform receives universal corrections from the curved background, the ``tail effects'', that resum into the so-called ``Sommerfeld factor''. We develop a systematic framework for computing this gravitational Sommerfeld factor for scalar perturbations with the presence of tidal effects on the system. Using the worldline EFT, we recast the diagrammatic resummation as a solution to the $d$-dimensional wave equation with a localized source, and derive a closed-form expression for the Sommerfeld factor in terms of the EFT connection matrix. We prove that the phase of the Sommerfeld factor is exactly the same as elastic Compton scattering phase shift when there is no tidal dissipation. By combining the renormalization techniques in EFT with the Mano--Suzuki--Takasugi method in black hole perturbation theory, we analytically solve the Sommerfeld factor for both the magnitude and phase to $O(G^{10})$ for the $\ell = 0, 1, 2$ partial waves. We further establish a new renormalization group equation for the radiative multipole moments, whose exact solution yields an improved resummation of the waveform beyond the universal tail logarithms. These high-precision data and exact relations pave the way for future resummation models of the waveform.

We present a closed formula for the computation of static post-Newtonian corrections to the two-body gravitational dynamics at any odd order, assuming the lower-order results are known. The formula is derived within a correlation function framework and exploits the $\mathbb{Z}_2$ symmetry of the static sector, leading to a novel theoretical interpretation of the factorization theorem. As an application, we compute the gravitational interaction of two compact coalescing objects at the seventh post-Newtonian order in the static limit, which receives contributions from seven-loop graphs at order $\mathcal{O}(G_N^8 v^0)$, and find complete agreement with the results obtained using the diagrammatic approach of the factorization theorem.

In this work, we study of the algebraic-hyperbolic formulation of the Einstein constraint equations for numerically constructing initial data sets for inhomogeneous cosmological space-times with $\mathbb{T}^3$ topology. We implement a pseudo-spectral method of lines based on the discrete Fourier transform and find that the scheme exhibits pathological instabilities. Through linear stability analysis, we prove that the instabilities are unavoidable for any space-time sufficiently close to FLRW while we find that this approach can be stable for Gowdy space-times depending on the initial time choice. Additionally, we present numerical evidence that certain subclasses of the algebraic-hyperbolic formulation, when combined with a Fourier-based method of lines, are numerically stable, thus offering a potential new path for computing initial data sets for inhomogeneous cosmological space-times.

The physical effect of condensation of a classical spinor field at the event horizon is under consideration. The corresponding solution is sought for the set of the Einstein-Dirac equations. It is shown that in this case there arises a black hole with a $\delta$-like classical spinor field concentrated at the event horizon.

We analyze the spherical harmonic mode amplitudes of quasicircular, nonprecessing binary black hole mergers using 275 numerical relativity simulations from the SXS, RIT, and MAYA catalogs. We construct fits using the leading-order post-Newtonian (PN) dependence on intrinsic parameters, replacing the PN velocity with fit coefficients. We compare these to polynomial fits in symmetric mass ratio and spin. We analyze $(\ell, m)$ modes with $\ell \leq 4$ from late inspiral [$t = -500M$ relative to the $(2,2)$ peak] to postmerger ($t = 40M$). For nonspinning systems, the $(2,2)$, $(2,1)$, and $(3,3)$ modes retain the leading-order PN dependence on mass ratio throughout the merger. Higher-order modes deviate from the PN dependence only near and after the merger, where polynomial fits of degree $N \leq 3$ can capture the amplitude behavior up to $40M$. For aligned-spin systems at fixed mass ratio, the $(2,1)$ mode retains its PN spin dependence, while the $(3,2)$ and $(4,3)$ modes exhibit a quadratic spin dependence near merger. The PN-inspired fits lose accuracy with increasing mass ratio, particularly near merger. Results broadly agree across catalogs, though discrepancies appear in the $(3,1)$, $(4,2)$, and $(4,1)$ modes, likely from resolution differences. Our results clarify the extent to which PN structure persists in mode amplitudes. Although the fits cannot be fully interpreted within the PN formalism near merger, low-degree polynomial corrections to the PN amplitude Ansätze can capture strong-field behavior, enabling closed-form and efficient modeling of waveform amplitudes in this regime.

The quantum description of a gravitationally collapsed ball of dust proposed in Ref.~\cite{Casadio:2023ymt} is characterised by a linear effective Misner-Sharp-Hernandez mass function describing a matter core hidden by the event horizon. After reviewing the original model and some of its refinements, we investigate the quasi-normal mode spectrum of the resulting spacetime and compare it with the Schwarzschild case. Computations are performed within the WKB approximation, based on the Padé approximants up to thirteenth order. Our analysis shows that deviations from the Schwarzschild spectrum are sensitive to the quantum nature of the core surface.

In this article, we explore the Rényi law constraints on black hole merger in Gauß-Bonnet (GB) gravity. Specifically, we consider the case of static solutions in five-dimensional (5D) Anti-de-Sitter (AdS) spacetime and study the constraints on merger of two equal mass black holes. We calculate the general Rényi entropy expression and utilize it to study the bounds on the final black hole mass post-merger. We study its variation with the Rényi parameter. We also compare the results with those for black holes in General Relativity (GR). We find that the GB term has a significant impact on the bounds for black hole merger. The bounds for GB gravity become weaker for the zeroth order Rényi entropy and stronger for higher order Rényi entropies in comparison to GR.

Accurate modeling of gravitational waveforms from compact binary coalescences remains central to gravitational-wave (GW) astronomy. Post-Newtonian (PN) approximations capture the early inspiral dynamics analytically but break down near merger, while numerical relativity (NR) provides the accurate yet computationally expensive waveforms over limited parameter ranges. We develop a physics-informed neural network (PINN) framework that learns corrections mapping PN dynamics and waveforms to their NR counterparts. As a demonstration of the approach, we use the TaylorT4 PN model as the baseline, and train the network on a remarkably small dataset of only eight hybridized NR surrogate waveforms (NRHybSur3dq8) to learn higher-order corrections to the orbital dynamics and waveform modes for nonspinning noneccentric systems. Physically motivated loss terms enforce known limits and symmetries, such as vanishing corrections in the Newtonian limit and suppression of odd-$m$ modes in equal-mass systems, promoting consistent and reliable extrapolation beyond the training region. We simultaneously incorporate corrections that account for the different meaning of mass parameters in PN and NR descriptions. The learned corrections significantly reduce the phase and amplitude error through the inspiral up to about $200M$ before the merger. This approach provides a differentiable and computationally efficient bridge between PN and NR, offering a path toward waveform models that generalize more robustly beyond existing NR datasets.

In this article, we performed Simpson-Visser (SV)-regularization scheme to Anti-de Sitter (AdS) black holes and then studied thermal properties of the resulting spacetime geometry. We considered the validity of the first law of black hole thermodynamics in this case and derived an entropy formula consistent with this new regular geometry. Next, we carried out the free energy analysis and studied the phase structure of these black holes. We discovered non-trivial phase transition properties dependent on the SV-regularization parameter. We also considered the validity of the second law of black hole thermodynamics and analyzed a merger scenario of two equal mass SV-regular black holes. In particular, we investigated the impact of the SV-regularization parameter on the constraints on post-merger black hole mass. Intrestingly, we found that the bounds initially increase and then fall sharply with increasing the SV-regularization parameter. All results are compared with standard black holes for vanishing SV-regularization parameter.

Large-scale simulations of celestial systems are based on approximations or modifications of classical dynamics. The approximations are with ``particle-mesh'' (PM) substitutions of the attractions from objects far away, or one modify the Newtonian accelerations (MOND) or the gravities (MOGA). The PM approximation and MOND modification of classical dynamics break the invariances of classical dynamics. The simple three-body system (TBS) is the simplest system to test the approximations and modifications of celestial dynamics, and it is easy to implement on a computer. Simulations of the TBS show that the PM approximation and MOND destabilize TBS. In contrast, the MOGA modification of gravity by replacing Newton's inverse square attraction with an inverse attraction for far-away interactions stabilizes the system. The PM approximation and the MOND modification of classical dynamics do not preserve the momentum and angular momentum of a conservative system exactly, and PM does not obey Newton's third law. Although the errors and shortcomings of these PM approximations and MOND modifications are small, they cause the instability of the regular dynamics.

Detection of entanglement through the Newtonian potential has been claimed to support the existence of gravitons, by extrapolating to a thought experiment which demonstrates that complementarity and causality would be in conflict unless quantum fluctuations exist. We critically assess this consistency argument using scalar field models. We show that whether complementarity or no-signalling is violated when quantum fluctuations are neglected, depends on how this approximation is taken, while in both cases entanglement is generated locally in spacetime. We clarify that the correct reading of the paradox requires making a clear distinction between two notions of causality violation: Newtonian action-at-a-distance and the quantum mechanical no-signalling; the latter is pertinent while the former is not. We conclude that the thought experiment (a) does not add to the epistemological relevance of entanglement through Newtonian potentials (b) lends support for the existence of gravitons, if retardation effects are detected in entanglement through gravity.

In this paper, we investigate the evolution of the early universe within an emergent fractional cosmological framework. The underlying formulation is conceptually rooted in generalized measure constructions, closely related to fractal geometries and scale-dependent effective dimensions. By constructing a suitable fractional potential, we show that the cosmological evolution naturally originates from a non-singular pre-inflationary regime. Inflation arises dynamically without introducing an external scalar field and emerges as a stable attractor, exhibiting similarities with plateau-type inflationary scenarios. By analyzing the dynamical transition, we determine the end of inflation and establish a meaningful relation between the number of e-folds and the fractional parameter $\alpha$, ensuring consistency with observations and addressing the horizon problem. Moreover, the model admits a graceful exit from inflation, followed by an exact radiation-dominated solution with the standard time dependence and an $\alpha$-dependent normalization.

We investigate the detectability of Gravitational Wave (GW) modes (emitted by black-holes and neutron stars) by third generation, ground-based gravitational wave detectors planned to be operational in the next decade. Our analysis focuses on the Cosmic Explorer and Einstein Telescope projects, which are expected to have arm lengths of tens of kilometers and to experience the amplification of a gravitational wave signal at their Full-Spectral Range (FSR) frequencies. We find that both projects will also observe with good Signal-to-Noise ratio (SNR) the elusive {\it w-modes}, which are expected to be emitted at these frequencies by spinning neutron stars.

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.

In this paper, as an application of the `Complexity = Volume' proposal, we calculate the growth of the interior of a black hole at late times for finite cutoff JT gravity. Due to this integrable, irrelevant deformation, the spectral properties are modified non-trivially. The Einstein-Rosen Bridge (ERB) length saturates faster than pure JT gravity. We comment on the possible connection between Krylov Complexity and ERB length for the deformed theory. Apart from this, we compute the emission probability of baby universes in the deformed theory and find that it changes due to the deformation parameter only if we turn on Lorentzian evolution. We also find that the saturation time of the deformed theory relative to the undeformed one depends on the inverse temperature. We also highlight the subtleties involved in the dual matrix model and comment on the possible one-cut universality. Finally, we comment on the possible correction to the volume of the moduli space arising from the non-perturbative correction of the spectral curve induced by the finite boundary cutoff.

Axion inflation is a well-motivated model of cosmic inflation with a rich phenomenology. The abundant production of gauge fields during axion inflation notably sources a stochastic gravitational-wave (GW) background signal, which nourishes the hope that future GW searches might have a chance to probe the model. In this paper, we scrutinize GW production during axion inflation in the gradient expansion formalism (GEF), a powerful numerical technique that captures the nonlinear dynamics of the system in the limit of vanishing axion gradients. We focus on {single-field} axion inflation coupled to a pure Abelian gauge sector, i.e., pure axion inflation (PAI), and perform the first-ever {detailed} parameter scan of GW production in the Abelian PAI model close to the onset of strong backreaction. {We approximate the axion potential around its minimum by a quadratic mass term and study the tensor modes that exit the Hubble horizon as the axion rolls down this potential.} Remarkably enough, we find that GW signals within the reach of future GW interferometers can only be realized in parameter regions that also lead to strong backreaction and that are in conflict with the upper limit on $\Delta N_{\rm eff}$, i.e., the allowed energy density of dark radiation. This observation defines a clear target for future lattice studies of axion inflation that may confirm or improve the predictions of our GEF benchmark.

Loop contributions to cosmological correlators and to the associated wavefunction are of key theoretical and phenomenological interest. Here, we investigate and compare different renormalisation schemes proposed in the literature to handle ultraviolet divergences and develop new schemes adapting $\eta$ regulators to de Sitter spacetime. We focus on one-loop contributions to the quadratic wavefunction coefficient of a shift-symmetric massless scalar in de Sitter spacetime, which is a good toy model of primordial curvature perturbations. We show that different implementations of dimensional regularisation agree with each other and with unitarity and scale invariance in the final renormalised result. Imposing unitarity in the form of the cosmological optical theorem, we define a class of unitary and analytic $\eta$ regulators that agree with dim reg but feature considerable technical and conceptual simplifications. We show that the imaginary part of all one-loop wavefunction coefficients is universally fixed in terms of the logarithmic running of the real part, under the assumptions of scale invariance, Bunch-Davies vacuum and light bulk fields. Our work resolves discrepancies in the literature, establishes regulator-independent predictions for the imaginary part at one loop, and provides a practical framework for computing quantum contributions to cosmological correlators.

Heavy particle effective theory applied to spinning black holes provides a natural framework in which propagators linearize and numerators exponentiate. In this work, we exploit these two features to introduce Kerr generating functions, which describe the scattering of any probe on a Kerr black hole background to all loop orders. These generating functions can be used to perform the tensor reduction of multi-loop integrands simply by differentiation with respect to the spin. As a first application of the Kerr generating functions, we study the leading non-linear tidal effects of a neutron star in a Kerr black hole background. We organize the integrand by the helicity configuration of the exchanged gravitons and provide compact all-loop-order results for several helicity sectors and a full four-loop $\mathcal{O}(G^5)$ result for the leading non-linear tidal operators.

Axion inflation represents an intriguing source of gravitational waves (GWs) from the early Universe. In a companion paper, arXiv:2508.00798, we previously leveraged the gradient expansion formalism (GEF) to investigate pure axion inflation (PAI), i.e., axion inflaton coupled to a pure gauge sector. In this paper, we extend our analysis to fermionic axion inflation (FAI), i.e., we allow for the presence of fermions in the gauge sector. PAI predicts a strongly blue-tilted GW spectrum; in our GEF benchmark study, all parameter regions leading to observable GWs turned out to violate the upper limit on the number of extra relativistic degrees of freedom, $\Delta N_{\rm eff}$. As we demonstrate in this paper, the situation is different for FAI: Schwinger pair creation of the charged fermions results in a damping of gauge-field production, which attenuates the GW signal. As a result, the GW signal from FAI can fall into the sensitivity reach of LISA and ET without violating the upper limit on $\Delta N_{\rm eff}$. This result notably applies to the arguably most realistic variant of Abelian axion inflation, in which the axion couples to the hypercharge sector of the Standard Model. Besides, we discuss GW emission from the fermion gas, which may further enhance the total GW signal but which also requires a more quantitative investigation in future work. Additionally, we identify a new backreaction regime in which fermion production moderates the axion--vector dynamics. In this regime, the axion velocity and all energy-density components exhibit oscillations analogous to the strong backreaction in PAI, but here, the oscillations occur around the slow-roll trajectory and are damped by the presence of charged fermions. These observations define again an interesting GEF benchmark for future lattice studies.

Posterior inference on the more than a dozen parameters governing a gravitational wave (GW) event is challenging. A typical MCMC analysis can take around $100$ CPU hours, and next generation GW observatories will detect many thousands of events. Here we present a thorough comparison of the accuracy and computational cost of the Fisher Matrix, Derivative Approximation for Likelihoods (DALI) and traditional MCMC methods. We find that using DALI, which extends the traditional Fisher Matrix (FM) method to higher orders, allows for a good approximation of the posterior with a $55$ times smaller computational cost, and that the cost-benefit of the doublet-DALI is better than that of the triplet-DALI. We also show that the singlet-DALI, a hybrid MCMC-Fisher method, is much more accurate than the traditional FM and 10 times faster than the doublet-DALI. A large effort has been invested in forecasting the science case of different detector configurations, and the ability of making fast yet accurate estimations of the posteriors is an important step forward. We also introduce version \texttt{1.0} of the public \texttt{GWDALI} code, which incorporates automatic differentiation, modern waveforms and an optimized parameter decomposition.

Motivated by cosmological observations, we push the cosmological bootstrap program beyond the de Sitter invariance lamppost by considering correlators that explicitly break scale invariance, thereby exhibiting primordial features. For exchange processes involving heavy fields with time-dependent masses and sound speeds, we demonstrate that locality in the bulk implies a set of integro-differential equations for correlators on the boundary. These scale-breaking boundary equations come with a built-in memory kernel in momentum-kinematic space encapsulating the universe's evolution during inflation. Specialising to heavy fields with sinusoidal masses such as those found in axion monodromy scenarios, we show that a powerful synthesis of microcausality and analyticity allows an analytical solution of these equations at leading order in the amplitude of mass oscillations. Meanwhile, we also unveil non-perturbative information in the integro-differential equations by resumming apparent infrared divergences as parametric resonances. In addition, we provide a first-of-its-kind example of numerical bootstrap that directly maps out the solution space of such boundary equations. Finally, we compute the bispectrum and uncover, in the squeezed limit, a scale-breaking cosmological collider signal, whose amplitude can be exponentially enhanced (with respect to the Boltzmann suppression) due to particle production triggered by high-frequency mass oscillations.

We propose a new action for entanglement entropy in the framework of the AdS$_{3}$/CFT$_{2}$ correspondence. This action is constructed directly from the entanglement entropy of the CFT$_{2}$, and we show that the Einstein equations of AdS$_{3}$ gravity can be derived from it. In the near-coincidence limit, using Riemann normal coordinates, the action reduces to a string worldsheet action in a curved background that naturally includes the symmetric spacetime metric, an antisymmetric Kalb-Ramond field, and a dilaton. The Kalb-Ramond field gives rise to a string charge density, from which we demonstrate that bit threads can be exactly reproduced. This correspondence provides a clear physical interpretation of bit threads. Exploiting this correspondence, we establish explicit relations between the emergent string worldsheet and the Ryu-Takayanagi (RT) surface, providing new insights into entanglement entropy. In particular, entanglement entropy can be computed from open string charge, while Bekenstein-Hawking entropy arises from closed string charge through open-closed string duality. These results suggest a unified picture in which the Susskind-Uglum conjecture, open-closed string duality, and the ER=EPR proposal emerge as equivalent manifestations of the same underlying principle. Finally, we propose a quantization of the RT surface, pointing to a possible connection with loop quantum gravity that refines Wall's conjecture.

We present an analytical study of the interior structure of hairy rotating black holes in three-dimensional Einstein gravity, minimally coupled to a complex scalar field with a super-exponential potential. The interior dynamics of these black holes are characterized by an infinite sequence of Kasner epochs, separated by inversion and transitions, each of which admits an analytical description. We derive an explicit analytical expression for this infinite sequence of epochs. At late interior times, the geometry evolves into a curvature singularity, despite the local resemblance of each Kasner epoch to a regular Milne universe on a circle. These results reveal an interior structure richer and more complex than that of its 4D static black hole counterparts.

We investigate the angular anisotropy of the Hubble constant using the Cosmicflows-4 catalogue, with particular emphasis on three issues often treated only implicitly in the literature: the statistical formulation of the Hubble--Lemaître relation, the internal consistency of the working sample, and the role of peculiar-velocity corrections. Rather than working in luminosity-distance space, we adopt a logarithmic formulation based directly on distance moduli, thereby preserving the Gaussian error properties of the measured quantities. We first subject the catalogue to internal consistency tests, including the depth dependence of $\langle \log H_0 \rangle$ and the behaviour of residual skewness and kurtosis across radial shells, and use these diagnostics to define conservative subsamples minimally affected by selection effects, namely $\mu \in [31,36]$ and $z \in [0.03,0.06]$. Within these ranges, we reconstruct angular maps of $\log H_0$ and fit them with a spherical-harmonic expansion up to octupole order. We find a statistically significant anisotropic signal in the uncorrected CF4 data, dominated by a dipole and favoured over a monopole-only model by Bayesian evidence. However, when peculiar-velocity-corrected data are used, the anisotropy amplitude is strongly reduced, especially at lower depths, while only a weaker residual signal survives at larger distances. We also test for a monotonic radial evolution of the dipole, as expected in some differential-expansion scenarios, but find no robust evidence for such a trend. These results indicate that the anisotropy is driven primarily by local velocity flows and catalogue/survey structure, rather than by a large-scale breakdown of isotropic expansion. Finally, we show that although such anisotropy may affect local determinations of $H_0$, its impact on the global Hubble tension is likely limited.

We study a spacetime obtained from the semi-classical backreaction computed via the Thermofield dynamics approach in the Poincare patch of de Sitter spacetime. The resulting bulk equation takes the Whittaker form and we examine two distinct applications. At leading order, the co-moving curvature perturbations are shown to match a constant-roll model in the frozen attractor regime, corresponding to a UV enhancement of the spectrum with $n_S \sim 2$. This blue tilt arises only for modes exiting the horizon during a transient late-time phase of inflation and therefore does not affect perturbations in the CMB scale. In the holographic context, we compute the CFT two-point function at the future boundary, and away from it we construct the flow-equation of the dual QFT that matches the beta-function of the Sp(N ) model in three dimensions.

Modelling structure formation across the full dynamical range of the Universe remains a major challenge in cosmology. This difficulty originates from a fundamental limitation of geodesics in general relativity: a one-parameter family of geodesics can cease to be geodesic at a finite time. This implies that the conventional point-particle approximation is not the primary issue; rather, the breakdown of geodesic flow restricts a consistent description across scales. We develop a covariant multi-scale framework that resolves this problem by decomposing spacetime into hierarchical regions separated by matter horizons. We show how to match shared boundary consistently at the level of the action, leading to a covariant backreaction contribution. The resulting construction provides a first-principles theoretical foundation for cosmological zoom-in simulations and yields an effective energy-momentum tensor capturing the impact of the geometric backreaction effect. As an application, we demonstrate that this backreaction naturally produces flat galaxy rotation curves without invoking an additional dark matter component. Our results establish a new perspective on nonlinear structure formation, in which long dynamical range is resolved through a hierarchy of discrete geodesic domains.

Conformally-invariant and pure, scale-invariant theories of gravity are particularly interesting in four or higher dimensions. Yet, in contrast to their four-dimensional counterparts, theories in higher dimensions are significantly more difficult to study. In these proceedings, following our recent work, we will formulate such theories in d dimensions, present an elegant way to handle them, and show that imposing invariance under scale or conformal transformations gives rise to entirely different properties when compared to their four-dimensional analogues.