Papers

Accurate predictions of gravitational wave signals from asymmetric compact binaries are accessible through black hole perturbation theory and self-force calculations. Faithful waveform models will require contributions from first- and second-order terms in the small mass-ratio expansion. The problem of second-order Kerr perturbations is exacerbated by non-separability of the metric perturbation equations and non-linear mode coupling, which motivates this $m$-mode approach. This work moves towards the eventual goal of second-order Kerr perturbations by calculating first-order Schwarzschild metric perturbations via $m$-modes in the frequency domain for the first time. We solve the Lorenz gauge field equations as a system of coupled elliptic partial differential equations that govern each $m$-mode. Our Mathematica code implements a second-order finite difference representation of the field equations, which we solve as a sparse linear algebra problem. Regularization near the small body is achieved through the effective source method, and our presentation introduces a new puncture expansion of the singular field for a point mass in Kerr spacetime. Issues related to problematic near-horizon behavior are explored and then mitigated by applying sophisticated near-horizon boundary conditions. Our results illustrate the features of each component and $m$-mode of the metric perturbation, and we are able to calculate gravitational wave energy fluxes with sufficient accuracy to enable future second-order self-force calculations.

We present several representations of the Schwarzschild spacetime. Some of these are classical, such as the embedding, Tortoise, and Kruskal representations. The latter two motivate the introduction of pulsating coordinates (or the Diamond representation), a compact approach recently proposed for spherically symmetric static metrics. We then introduce the Golden representation for the Schwarzschild spacetime, where what we call the Fibonacci metric, and the golden ratio, become ubiquitous. We conclude by offering some visual and physical interpretations of this approach.

Four-fermion interactions appear in effective descriptions of particle physics, many-body systems, and gravitational theories with fermions. Although the same local operator may enter perturbative scattering, a vacuum Nambu-Jona-Lasinio (NJL) instability, or finite-density Bardeen-Cooper-Schrieffer (BCS) pairing, these regimes are distinguished by their interaction channels, quadratic kernels, and quantum states. We give a pedagogical functional account of these distinctions and compute the local one-loop contribution of a scalar-channel NJL mean field to the energy-momentum tensor in curved spacetime. We first display the state data in the in-out functional and construct the closed-time-path functional required for an in-in expectation value. For the NJL saddle, a Hubbard-Stratonovich field shifts the fermion mass, and the parity-even Dirac determinant generates local volume, curvature, and curvature-squared operators. We find the covariant quantum effective action before specializing to a spatially flat FLRW background and derive the corresponding energy density and pressure. The constant-condensate limit agrees with the direct flat-space mean-field calculation. We also explain which additional state and channel data are required for finite-density BCS pairing and comment on renormalization conditions in curved spacetimes.

The Lambert $W$ (LW) model for the cosmic fluid equation of state was proposed by S. Saha and K. Bamba in 2019-2020. A recent (early 2026) paper by Dubey, et al, carries out a new fit of the LW model to observational data, in order to estimate the model's parameters. That paper exhibits a formula for the logarithm of the relative Hubble factor at redshift $z$, $\ln(H(z)/H_0)$, which is based upon a numerical integration. That integral can be evaluated analytically, and we present the details in this working paper. The resulting analytic expression for $H(z)/H_0$ may be convenient for exploration of the LW model. We present two approximation formulas for the Lambert $W$ function, highly accurate for redshifts $z$ between 0 and 3, which may be useful for researchers who do not have ready access to a function library with the Lambert $W$ function. We also present a simplified proof of the analytic formula for another logarithmic integral which may be useful for exploring some variants of the LW model.

The general relativity may not be the final theory of gravity. One possible way to look for the gravity theory beyond general relativity is considering variable gravitational constant. Based on the quantum field theory, the gravitational constant as the coupling constant of gravity interaction may change along with the energy scale. Such scale dependent behavior of the gravitational constant can be well described by the functional renormalization group. In the current work, we investigate such behavior systematically. Firstly we find that such behavior is qualitatively independent of interactions such as the electromagnetic interaction included or not. But quantitatively the behavior is governed by two to-be-determined parameters. In general a limit scale may be introduced by the scale dependence of the gravitational constant. If we assume all physical scales are feasible, the two parameters are limited in some special regions. And more we compare the scale dependence behavior to the existing observations. We find the observation results constraint the two parameters strictly.

We investigate the nonseparability of multipartite bosonic and fermionic $GHZ$ and $W$ states in a causal diamond spacetime using the Abe-Rajagopal (AR) $q$-conditional entropy. The finite lifetime of the observer gives rise to a causal diamond horizon, which induces an Unruh-like thermal effect and leads to a nontrivial restructuring of nonseparability in $N$-partite systems. Our main result is that the thermal effect can enhance a net nonseparability of fermionic $W$ states, in sharp contrast to the general expectation that relativistic thermalization leads to a monotonic degradation of bosonic nonseparability. In addition, we find that fermionic nonseparability is generally more robust than its bosonic counterpart under causal diamond restrictions. Among different entangled resources, $GHZ$ states exhibit stronger nonseparability and greater robustness than $W$ states under identical causal conditions. We further show that the nonseparability of $W$ states decreases with increasing particle number $N$, whereas that of $GHZ$ states remains independent of $N$ in causal diamond spacetime. These results demonstrate that particle statistics, entanglement structure, and observer lifetime jointly determine the persistence of nonseparability in causally restricted spacetimes, providing insights for relativistic quantum information processing.

In Penrose's nonlinear graviton construction, a self-dual spacetime arises as the moduli space of holomorphic twistor lines in curved twistor space, whose explicit parametrization is concretely given by the incidence relation. We demonstrate a concrete local construction of the incidence relations for self-dual black hole spacetimes in Kerr-Schild coordinates: Eguchi-Hanson, self-dual Taub-NUT, and self-dual Plebański-Demiański. This is facilitated by implementing the Dunajski-Mason recursion in the framework of Plebański's second heavenly equation, for which we explicitly find the Plebański scalar. Our results describe closed-form formulae. Notably, for the self-dual Taub-NUT solution, the exact incidence relation exhibits linear dependence on the gravitational coupling. The construction of zero-rest-mass fields on self-dual black hole backgrounds is briefly sketched as an application.

We compute, up to 4th post-Newtonian (4PN) order, the gauge-invariant stability criterion determining the innermost stable circular orbit (ISCO) for arbitrary-mass compact binaries with spins aligned with the orbital angular momentum. Our calculation, a perturbation analysis, incorporates spin-orbit and spin-spin contributions, both up to next-to-next-to-leading order, as well as leading-order cubic and quartic spin contributions, all calculated in prior works within the effective-field-theory (EFT) Hamiltonian formalism. In the test-mass limit, we recover the Kerr ISCO truncated at 4PN order. Estimating the ISCO shift at first order in the mass ratio and comparing our results with numerical gravitational self-force (GSF) calculations, we find good agreement for retrograde spin (the smallest discrepancy being obtained for maximal retrograde spin) and moderate prograde spin. For nearly maximal prograde spin, the PN approach fails to determine the ISCO, for it is close to the black hole (BH) horizon. We also estimate the ISCO shift due to the test-particle spin and compare our result with the exact prediction from the Mathisson-Papapetrou-Dixon (MPD) equations for a spinning particle orbiting a Kerr black hole. Finally, we discuss the stability and the ISCO of corotating black-hole binaries.

We show that black hole horizons with non-constant curvature can be constructed in any even dimension, when the source of the Einstein equations is given by the stress-energy tensor of a non-linear sigma model of a particular class

We develop a self-consistent framework that connects dark matter capture to the long term accumulation and structural evolution of neutron stars, allowing us to quantify the impact of capture driven asymmetric dark matter on gravitational wave observables over astrophysical timescales. We model cold, non-rotating neutron stars using a three layer polytropic EoS coupled to a dark matter component through the two fluid Tolman Oppenheimer Volkoff equations, and reconstruct the long term evolution using a time dependent dark matter capture formalism. By exploring a wide range of astrophysical conditions, including extreme environments designed to maximize the capture efficiency, we derive conservative upper bounds on the effects of dark matter accumulation over a Hubble time. Even under these deliberately optimistic assumptions, the accumulated dark matter component remains subdominant and induces limited structural modifications. In particular, dark matter accumulation increases the stellar compactness while suppressing the Love number and tidal deformability. Significant evolution occurs only in extreme Galactic center like environments over Hubble time scales, whereas for realistic Galactic or cluster dark matter densities the corresponding deviations remain negligible. We therefore conclude that capture driven dark matter accumulation is unlikely to produce detectable signatures in current or near future gravitational wave observations of neutron stars.

Asymptotic states of massive particles in electrodynamics and gravity are not uniquely defined because of the absence of a mass gap. Working in the KMOC formalism, we study the classical implications of this freedom in the dressing of massive particle states. We show that coherent-state dressings modify observables by a large gauge/BMS transformation. The associated coherent-state displacement operator can be completed into a conserved charge, the BMS charge in the gravitational case, which implements large gauge transformations on scattering data. The parameter of our dressing is directly the large gauge/BMS transformation parameter, and we explain that observables do not depend on monopolar and dipolar parts of the transformation parameter to all orders. Our construction is driven by soft factorization rather than by an underlying local symmetry, and we illustrate this by exhibiting the same structure in a scalar theory with no gauge symmetry. We explore the action of large gauge transformations on two-particle states for scalar, abelian gauge and graviton mediators, obtaining a universal shift of the impact parameter and clarifying the frame dependence of the radiated angular momentum vis à vis the frame-independence of the total angular momentum. The transformation connecting the canonical BMS frame, in which the Schwarzschild metric takes the Kerr-Schild form, to the intrinsic frame, in which it takes the De Donder form, illustrates these effects concretely.

Solving the Tolman–Oppenheimer–Volkoff (TOV) equations, together with the tidal perturbation equations, for large numbers of equation-of-state (EOS) samples is a major computational bottleneck in Bayesian inference of the dense-matter EOS, and this will become increasingly limiting as next-generation observatories deliver far larger and more precise datasets. We develop neural-network surrogates for the forward TOV mapping that predict neutron star mass, radius, and tidal deformability simultaneously and directly from the EOS parameters and central density. We train and compare two architectures: a conventional feedforward network and a residual network, the latter of which, to our knowledge, has not previously been explored for TOV surrogate modeling. Trained on a piecewise polytropic EOS parameter space, both networks reproduce the numerical solutions to high accuracy, with the coefficient of determination exceeding 0.999 for all three observables, while accelerating the evaluation of stellar observables by roughly two orders of magnitude relative to direct numerical integration. We find that both architectures achieve excellent predictive accuracy at the network sizes considered here, with the residual network providing a modest improvement in accuracy over the feedforward network at the expense of slightly longer inference times. The overall performance differences remain small, indicating that a feedforward network already has sufficient capacity for this mapping while residual connections offer only incremental gains. Nevertheless, the residual architecture provides a robust baseline for future extensions to richer EOS parameterizations or higher-dimensional regression tasks. The resulting surrogates are well-suited to large-scale Bayesian EOS inference and population studies, where repeated TOV evaluations would otherwise dominate the computational cost.

Astrophysical black holes (BH) are not isolated, but embedded in matter supplied by their host galaxies. We study how the shape of a surrounding dark matter (DM) halo modifies the ringdown and tidal response of an asymptotically flat, static, spherically symmetric BH. The halo is modelled as an anisotropic Einstein cluster with vanishing radial pressure and a generalized $(\alpha,\beta,\gamma)$ density profile, supplemented by an inner cut-off near the BH and, where required, an outer tidal truncation. We derive the axial gravitational perturbation equation and compute the quasinormal mode (QNM) spectrum using sixth-order Wentzel-Kramers-Brillouin (WKB) methods and time-domain evolutions. The halo redshifts both the oscillation frequency and the damping rate, by an amount set not only by the halo compactness but also by the profile parameters: the inner slope $\gamma$ dominates for centrally concentrated halos, while $\alpha$ and $\beta$ give subleading but profile-dependent corrections. In the eikonal limit, the shift is governed by a single redshift integral encoding the halo mass distribution outside the light ring, explaining the close correspondence between the QNM frequencies, the light ring frequency, and the Lyapunov exponent. We also show that different combinations of compactness and profile shape can yield nearly degenerate ringdown spectra. Time-domain evolutions confirm the WKB frequencies and display the expected late-time Price law decay, with an intermediate tail controlled by the outer density falloff for slowly decaying profiles. Finally, we compute the static axial tidal Love number and show that it probes the halo with a radial weighting different from the ringdown sector. The combined ringdown and tidal response therefore provides a possible way to distinguish environmental effects from genuine deviations of the vacuum BH geometry.

Classical fractons are Hamiltonian systems that can develop attractors after projection onto configuration or shape variables, although the full phase space admits none. We study a scale-invariant, dipole-conserving two-parameter family of fracton Hamiltonians $H_{\alpha,\beta}$. By separating coordinates into scale and shape, we obtain autonomous shape dynamics that admit fixed points which leave a purely scale evolution of the form $R(t)\propto |t|^{\alpha/(\alpha-\beta)}$. The shape fixed points, which determine the distribution of the expanding particles, are central configurations of power-law Riesz potentials. The distinguished model $(\alpha,\beta)=(-2,1)$ is unique: its scale evolution takes the Einstein-de Sitter form $R(t)\propto |t|^{2/3}$, its fixed-point equation is the equal-mass Newtonian central-configuration, its large-$N$ distribution is a homogeneous ball, and its homothetic trajectories admit a zero-energy Newtonian gravitational dual. The fixed points are locally stable, and simulations at moderate $N$ approach them from random initial data. Large $N$ simulations reveal a richer class of fixed-points: bound clusters of approximately fixed physical size retain internal motion, while their centers approach unequal-mass Newtonian central configurations and preserve large-scale homogeneity. A scale-separation conjecture yields an effective unequal-mass fracton dynamics for the centers and a corresponding zero-energy Newtonian gravitational dual. Trajectories generically exhibit a bidirectional arrow of time: scale and shape complexity grow away from a Janus point, while Boltzmann entropy grows logarithmically. Together, these features reproduce the salient structure of a flat matter-dominated cosmology. In the distinguished fracton model, all these cosmological analogues emerge as attractor properties, making it a toy model for cosmological dynamics without fine-tuning.

Strongly lensed gravitational waves (GWs) are powerful probes of substructure in the lens. Intermediate-mass black holes (IMBHs) are postulated to be efficient lenses that may distort the lensed waveforms of currently detectable stellar-mass compact binaries, as hinted by GW231123. Assuming that IMBHs are located in globular clusters (GCs), we compute the rate at which they would affect strongly lensed repeated chirps produced by galaxy-scale lenses, considering a compound lens system. Exploring different astrophysical model assumptions and lensing criteria, we find that the relative rate is at most 1/1000 and decays to 1/10,000 for our fiducial optimistic scenario. At high magnifications, $\mu$ > 100, the relative rate approaches 1%, but these cases are intrinsically rare in absolute value. Our results imply that GW lensing by IMBHs and GCs is unlikely, disfavoring such an interpretation for GW231123. In turn, they point towards lensed GWs being a clean probe of dark matter substructures and primordial black holes.

We report a multi-pipeline follow-up study of the continuous gravitational-wave (CW) outlier identified by the Ming et al. Einstein@Home directed search for the young supernova remnant G347.3-0.5 (containing the central compact object RXJ1713.7-3946). The outlier was initially identified in LIGO data from the O3a observing run and followed up with the addition of O3b and O4a data by the Einstein@Home pipeline, with O4a producing weaker evidence. Here, we show extended data quality checks and results from three pipelines that have independently investigated this outlier, including the newly released O4b data set. We can robustly recover the outlier in O3, while we find no evidence for a related standard CW signal in O4a (consistent with Ming et al.) and O4b data. This work serves as a useful test case for future multi-pipeline follow-ups of CW candidates that aim to investigate their astrophysical or noise nature, and it is therefore an important step in preparation for the first CW detection.

Large numerical-relativity surveys require compact-binary initial data that are both spectrally accurate and inexpensive to construct, including for systems with unequal masses and misaligned spins. We present \celephais, a compact-object initial-data code built on the Kadath spectral library, that constructs binary-neutron-star and black-hole–neutron-star initial data without imposing equatorial symmetry. The method exploits the sparse structure of the globally coupled multi-domain Jacobian and the approximate parity separation of fields. The assembled matrix is factored with MUMPS and reused as a refreshed right preconditioner in a Jacobian-free Newton–Krylov iteration, thereby avoiding dense storage. An adaptive $hp$–refinement scheme then concentrates resolution where the spectral tails are not yet resolved. For a mass-ratio-$20$ black-hole–neutron-star benchmark, the adaptive schemes recover the uniform-grid constraint accuracy with about three times fewer unknowns. We also extend the post-Newtonian force-balance estimate to arbitrary spin orientations and use it to initialise eccentricity reduction. Validation comprises binding-energy comparisons with post-Newtonian sequences, a precessing binary-neutron-star eccentricity-reduction test, and a full evolution whose waveform-reconstructed precession axis follows a post-Newtonian simple-precession model. These results establish an efficient route to spectrally resolved binary-neutron-star and black-hole–neutron-star initial data with arbitrary spin orientations.

Einstein Telescope (ET) will be a next-generation ground based interferometric gravitational-wave detector designed to explore the Universe to an unprecedented depth and detail. With its 10-15 km long arms, underground infrastructure, and advanced cryogenic technologies to suppress thermal noise, ET aims at achieving a sensitivity up to eight orders of magnitude better than current detectors such as Virgo, LIGO, and KAGRA. The coverage of the low-frequency band, starting at 2 Hz, will enable the observation of earlier inspiral phases of compact binary coalescences, enhancing early-warning capabilities and improving multi-messenger follow-up. However, this increased sensitivity also implies a higher susceptibility to environmental disturbances, particularly in the 2-10 Hz range where anthropogenic, seismic and infrastructural noise noise are most relevant. Therefore, understanding and mitigating environmental contributions are essential to fully exploit the scientific potential of ET. This chapter reviews the ongoing studies on environmental noise for ET, summarizes the main challenges related to site characterization and infrastructure design and outlines the strategies currently under development to ensure optimal detector performance.

This study investigates how dark matter in the background of the phantom field (DMPF) near a black hole influences neutrino flavor oscillations using a two-flavor model. It is found that gravitational effects are cancelled for radially moving neutrinos, causing the oscillation phase to increase with distance and mass-splitting, similar to flat spacetime. However, deflected neutrinos experience additional phase shifts due to dark matter, which slightly alters the mass-difference term and the total phase. Numerical analysis supports these findings and reveals a degeneracy between lens mass and dark matter parameters, affecting the transition probability curves based on source angle changes. Neutrinos modeled as Gaussian wave packets show that decoherence in a gravitational field is minimally influenced by dark matter, with the absolute neutrino mass determining the oscillation duration. Our findings imply that curved spacetime and dark matter significantly impact neutrino oscillations, offering potential insights into dark matter through neutrino astronomy in extreme environments.

We give a Lefschetz thimble definition of the Chern–Simons–Kodama wavefunctional in Lorentzian self-dual gravity with positive cosmological constant. By complexifying the connection and choosing the Lefschetz thimble attached to the self-dual de~Sitter saddle, Witten's analytic continuation of Chern–Simons theory replaces the real contour, on which the defining integral is at best conditionally convergent, by an absolutely convergent integration cycle and yields a controlled semiclassical expansion. The relevant integrand is the full holomorphic exponential $e^{I}$, with $I=\kappa Y_{\rm CS}+(\text{source})$, and the steepest descent flow is governed by the Morse function $h=\operatorname{Re} I$. In the homogeneous isotropic de Sitter reduction, the construction reproduces the Hartle–Hawking Airy wavefunction. In the Bianchi~IX truncation, we take the Lefschetz thimble attached to the expanding de~Sitter saddle (the contracting branch defines a conjugate Lefschetz thimble); within this sector, the symmetric configuration is the only critical point for $\Lambda>0$. The corresponding Lefschetz thimble contains one trace direction with the FRW Airy structure and two anisotropic shear directions that are real-Gaussian damped at leading quadratic order. This gives a finite Bianchi~IX wavefunction which, to leading order, is the FRW Airy factor multiplied by a real anisotropy Gaussian. Thus, the Airy behavior is not an artifact of the one-dimensional minisuperspace reduction, but the leading form of the wavefunction on the Lefschetz thimble. We also discuss how the Lefschetz thimble prescription interfaces with Lorentzian reality conditions.

We study single-field slow-roll inflation in metric-affine gravity with a scalar field non-minimally coupled to the non-Riemannian Ricci scalar and to the divergences of the torsion and nonmetricity vectors, a structure that generalizes the well-known Nieh-Yan term. By imposing projective coherence of the matter sector and solving the connection field equations, we integrate out torsion and nonmetricity and obtain an equivalent Einstein-frame formulation in which the metric-affine couplings are encoded in a modified kinetic function and potential. For the choice of coupling functions $\mathcal{A}(\phi) = M_P^2 + \xi \phi^2$ to the non-Riemannian Ricci scalar, $\mathcal{C}_i(\phi) = \xi_i \phi$ to the Nieh-Yan-like terms and a monomial Jordan-frame potential $\mathcal{V} \propto \phi^k$, we show that in the limit of a large positive effective Nieh-Yan-like coupling $\bar{\xi}$ the canonical field satisfies $\chi \sim \phi^2$, the Jordan-frame field values during inflation become sub-Planckian, and the Einstein-frame potential reduces to $U \sim \chi^{k/2}$. We compute the slow-roll predictions numerically for quartic and quadratic Jordan-frame potentials and compare them with the current CMB constraints from Planck, BICEP/Keck, ACT, and SPT. We find that intermediate values of $\bar{\xi}$ can restore the compatibility of non-minimally coupled Palatini inflation with observations: in the quartic case, the model predicts a tensor-to-scalar ratio within reach of next-generation CMB experiments for $\bar{\xi}\lesssim10^4$, while in the quadratic case the coupling cures the $\eta$-problem arising for $\xi \gtrsim 10^{-2}$ and yields viable predictions for $10^{-2}\lesssim\bar{\xi}\lesssim 10^2$. In the negative $\bar{\xi}$ regime, the model does not improve upon standard Palatini inflation, though it can still produce distinct, testable predictions.

We propose gravitational caloric theory (GCT) — an extension of general relativity that features a vector field $S_\mu$ sourced by and non-minimally coupled to the fluid sector while preserving covariant conservation of the standard fluid energy-momentum tensor. Our initial motivation is to trigger early dark energy (EDE) using the total fluid equation of state that encodes the cosmic radiation-matter transition. This mechanism provides a natural resolution of the EDE coincidence problem. The cosmological background dynamics are analyzed in detail by casting the evolution equations into dynamical-system form and, in relevant reduced cases, using Poincaré compactification to uncover the corresponding global phase-space structure. Beyond EDE, GCT admits two novel cosmological applications associated with critical points at infinity. Both arise from a class of energy-cancelling solutions in which conventional energy components preferentially excite $S_\mu$ rather than source spacetime curvature. One is a $\Lambda$-cancelling solution that realizes the self-tuning mechanism for the old cosmological constant problem. Yet it remains incomplete. The other is a fluid-cancelling solution that serves as the basis for our proposed early static hot Universe. In this scenario, $S_\mu$ offsets the gravitational effect of ordinary hot gas, yielding quasi-static expansion with a decreasing comoving Hubble radius that can address the horizon problem. This offers an alternative to inflation. Furthermore, its hot ingredient distinguishes this scenario from other quasi-static early Universe models and may leave observable signatures in primordial fluctuations. To probe the viability of GCT beyond cosmology, we further analyze linear perturbations about Minkowski spacetime and investigate static spherically symmetric (strong-field) systems. (Abstract abridged to meet arXiv limits.)

We investigate a geometric approach referred to as the Conformal Killing Gravity (CKG), in which the dark energy sector emerges naturally from the conformal Killing symmetry of the Robertson–Walker space-time. Within this framework, the divergence-free conformal Killing tensor behaves as an effective perfect fluid, giving rise to a dynamical dark-energy component whose density, pressure, and equation of state are uniquely determined by the underlying geometry, without introducing any empirical dark-energy parametrization. The resulting CKG model extends the standard $\Lambda$CDM cosmology through a single additional parameter while recovering the $\Lambda$CDM limit in the absence of the geometric contribution. We constrain the model using Planck PR4 (NPIPE) CMB temperature, polarization, and lensing observations, ACT DR6 CMB lensing, DESI DR2 baryon acoustic oscillation measurements, and the Pantheon$+$, DES-Dovekie, and Union3 Type Ia supernova compilations. The analysis shows that the CKG favors a quintessence-like dark-energy evolution with no evidence for phantom crossing, while the reconstructed equation of state rapidly approaches the cosmological constant at earlier cosmic times. Furthermore, the model predicts a future critical redshift in the range $-0.8 \lesssim z_c \lesssim -0.7$, indicating that the present cosmic expansion eventually reaches a turning point before the formal singular limit at $z=-1$. Since the geometric contribution modifies only the post-recombination expansion history, the sound horizon remains essentially unchanged and the model does not provide a complete solution to the $H_0$ tension. Our results demonstrate that the CKG provides a simple, physically motivated, and observationally favored framework for describing the late-time accelerated expansion of the Universe.

We report on a follow-up search for continuous gravitational waves (CWs) targeting sub-threshold candidates from the O4a LIGO-Virgo-KAGRA (LVK) all-sky all-frequency (ASAF) directed radiometer analysis. We analyze a total of $562$ ASAF candidates using Advanced LIGO data from the first part of the fourth LVK observing run. Each candidate comprises a narrow $1/32$ Hz frequency band paired with a ${\sim}13$ deg$^2$ sky pixel, defining the search parameter space for our analysis. Our search pipeline leverages the $F$-statistic matched filter equipped with a hidden Markov model to enable tracking of a potentially frequency-wandering CW signal. Of the 562 initial candidates, we obtain $21$ outliers with false alarm probability less than $5\%$ that survive all instrumental vetoes. None of the outliers are recovered at comparable statistical significance in the second part of the fourth observing run, from which we conclude that no convincing CW signals are detected. We estimate the sensitivity of our analysis by recovering simulated signals added to real detector data. Across the $20\text{--}1726$ Hz frequency band, our search achieves $95\%$ detection efficiency for strain amplitudes in the range of $h_0\sim (0.63\text{--}6.3)\times10^{-25}$ with respect to isolated neutron stars (NSs), and $h_0\sim (0.82\text{--}7.1)\times10^{-25}$ with respect to NSs in long-period ($>1$ yr) binary systems. The large range in sensitivity is due to the strong frequency dependence of detector noise, particularly at low frequencies.

Tidal excitations of stellar oscillation modes during binary neutron-star inspirals offer a powerful probe of the composition of dense matter at supranuclear densities. Chemical equilibration plays a crucial, but often neglected, role in stellar perturbation calculations. If the chemical equilibration timescale is comparable to the oscillation timescale, then viscous effects can damp the modes. If the reactions are fast, some modes can completely disappear since their restoring force vanishes. Typically, these calculations, however, assume either instantaneous chemical equilibrium or no equilibration (frozen composition). Motivated by this, we investigate the effects of finite reaction rates on the oscillation spectrum of neutron stars containing hyperonic matter. We calculate the dominant non-leptonic weak interaction rates and incorporate them into the relativistic perturbation equations through a complex, frequency-dependent dynamical sound speed. We show that finite-rate effects naturally manifest as bulk-viscous dissipation, modifying the properties of both the fundamental ($f$) and gravity ($g$) modes. We further examine the impact on the tidal response by matching stellar perturbations to near-zone boundary conditions, demonstrating how viscous dissipation gives rise to a tidal lag. These results provide a consistent framework connecting microscopic reaction rates and the resulting bulk viscosity to the tidal dynamics of compact binaries, and represent a step towards incorporating viscous dissipation into gravitational-wave models of binary neutron-star inspirals.

We consider the dynamics of a charged fermion in de Sitter space in the presence of a uniform background magnetic field, and discuss magnetic catalysis of chiral symmetry breaking using the Nambu–Jona-Lasinio (NJL) model. We evaluate the mode functions of the charged fermion field in this background by imposing the Bunch–Davies vacuum condition. The gap equation is solved in the mean-field approximation. We derive analytic expressions for the gap in several limiting regimes, such as the large-magnetic-field and large-curvature limits. We find that the curvature effect restores chiral symmetry, whereas the magnetic field enhances chiral symmetry breaking through the conventional mechanism of magnetic catalysis. The phase structure associated with chiral symmetry breaking is revealed by numerical calculations.

We discuss the impact of tensor-induced backreaction at second order in perturbation theory on primordial black holes production in single-field inflationary models, where the comoving curvature power spectrum is amplified by a transient ultra-slow-roll phase. Although the leading perturbative correction is mostly negligible in standard slow-roll evolution, it becomes important in non-attractor regimes, going in the direction of limiting the suppression of the first slow-roll parameter $\varepsilon$ and reducing the enhancement of the scalar power spectrum. We then go beyond the standard perturbative analysis by considering the background parameters as effective quantities with evolution self consistently determined by a closed system of backreaction equations. This analysis, which leads to a partial resummation of the effect beyond the perturbative treatment, confirms the limitation of the suppression of $\varepsilon$ by consistently showing how the effect remains important even after accounting for the effective evolution of the background in the evaluation of the backreaction itself. Finally, we discuss how, taking into account the tensor-induced backreaction, the fine-tuning associated with the value of the peak amplitude of the scalar power spectrum is strongly reduced.

We derive and investigate the reduced dynamics of a nonrelativistic quantum matter system interacting with quantized gravitational waves. Because gravitational radiation couples tidally to the mass quadrupole moment, we emphasize that the leading interaction is quadratic in the mechanical displacement. Rather than treating it as a complication to be removed by linearization, we retain this full quadratic dependence, which gives rise to two-phonon rather single-phonon processes typical in dipolar interactions. We clarify its relation to the effective linear coupling that often appears in optomechanical literature, but which conceals the delicate quantum signatures of the full quadratic coupling. Using the Born-Markov and secular approximations, we microscopically derive Lindblad master equations for the matter dynamics induced by graviton baths in multi-mode vacuum, coherent, number, thermal, and squeezed states. We treat the ultraviolet-divergent Lamb-shift Hamiltonian by an explicit renormalization procedure, with the mechanical frequency identified as the physical frequency. Remarkably, owing to the nature of the interaction, the matter Hilbert space decomposes into even- and odd-parity sectors for all bath states considered. For a coherent graviton bath, the decoherence is identical to that of the vacuum, while the bath one-point function produces a coherent-shift Hamiltonian that exactly reproduces the tidal interaction with a classical gravitational wave. For a vacuum graviton bath, we recover the coherence protection between the two lowest mechanical number states, while number and thermal graviton baths remove this protection and enhance decoherence, although the effect remains small for realistic parameters. By contrast, a squeezed graviton bath enlarges the coupled coherence structure, and gives rise to a novel, coherence-protected sector spanned by dressed dark states.

According to the no-hair theorem, the multipole moments of an electrically neutral black hole in general relativity are entirely determined by its mass and spin. However, this is not in general true for compact objects: The multipole moments of neutron stars or exotic compact objects can depend on their formation history and internal processes, which are encoded in an equation of state. Furthermore, their spin-induced multipole moments differ from those of black holes of the same mass and spin, leaving an imprint on the dynamics and emitted gravitational waves of the binary. Gravitational waves can thus be used to test the nature of compact binary coalescences. Here, we present a test of the spin-induced quadrupole and octupole moments of compact objects based on the flexible theory-independent (FTI) framework. FTI is a parameterized inspiral test of general relativity which enables the addition of post-Newtonian coefficient deviations to the gravitational-wave phase of a generic aligned-spin frequency-domain waveform model. We use this test on synthetic signals to study the measurability of spin-induced quadrupole and octupole moments. Next, we apply the test to a subset of signals observed by the LIGO-Virgo-KAGRA Collaboration. Lastly, we present forecasts for next-generation ground-based detectors, such as Einstein Telescope and Cosmic Explorer. Our estimates suggest that these detectors will be capable of placing stringent constraints on the spin-induced quadrupole and octupole moments of $\mathcal{O}(10^{-2})$ and $\mathcal{O}(10^{-1})$ respectively, which is two orders of magnitude tighter than current constraints, and thus on the nature of black holes in a compact binary coalescence.

The supermassive black hole Sgr A* at the Galactic center provides a unique opportunity to probe the distribution of environmental matter around black holes. In this work, we adopt the Hernquist-type environmental black hole spacetime, a non-vacuum exact solution of the Einstein field equations, as its gravitational model to describe the joint gravitational field of the black hole and its surrounding matter, with environmental effects characterized by the dimensionless compactness $C$ and the characteristic scale $\alpha$. We combine black hole shadow data with two sets of S2 star data provided by Do et al. and Gillessen et al., and constrain the model parameters using the Markov chain Monte Carlo method. At the 95% credible upper limit, the shadow-only data constrain $C < 1.498\times10^{-1}$.but provide no effective constraint on $\alpha$. The two S2 datasets yield $C<5.239\times10^{-5}$ and $C<1.303\times10^{-4}$, respectively, with $\alpha$ exhibiting a bimodal structure in both cases. After combining the shadow and S2 star data, the $C$ upper limits are tightened to $C<3.760\times10^{-5}$ and $C<1.073\times10^{-4}$, respectively. These results indicate that current observations rule out highly compact configurations of the environmental halo, while the obtained constraints are consistent with the typical compactness range of matter halos. However, $\alpha$ still exhibits a significant bimodal degeneracy, indicating that current observations are insufficient to uniquely determine the radial distribution of the environmental halo. Future observations of multiple stellar orbits may provide further insights into the radial structure of the environmental halo.