Recent measurements from the Atacama Cosmology Telescope (ACT) and the South Pole Telescope (SPT) have placed the strictest constraints on the primordial scalar perturbation spectrum, reporting a spectral index of $n_s\sim 0.967–0.98$ at 95% confidence level. This result indicates a stronger scale invariance of the scalar perturbation than earlier estimates, posing challenges for numerous inflation models. In this work, we propose a novel inflationary scenario based on Weyl scale-invariant gravity, where the quadratic curvature establishes the scale invariance of the scalar spectrum, while the higher-order extensions imprint the observed slight deviation. Specifically, the exponential curvature extensions are introduced to suppress the mass divergence of the inflaton. We find such a scenario naturally yields leading-order predictions of $n_s\simeq 1–3/(2N)\sim 0.97-0.975$ or $n_s\simeq 1–5/(3N)\sim 0.967-0.972$ for various models, in excellent agreement with the ACT/SPT constraints. This result builds a concrete bridge between theoretical and observational scale invariance, implying an enduring cosmic echo of the primordial symmetry.

We investigate two different definitions of a scalar field effective potential in quantum field theory in de Sitter spacetime: the standard textbook definition, and the constraint effective potential proposed by O’Raifeartaigh et al. in 1986. While these definitions are equivalent in Minkowski spacetime, they differ significantly in de Sitter spacetime. We demonstrate this by computing them both explicitly at one-loop order in perturbation theory. It is well known that the perturbative expansion of the standard effective potential fails to converge for light fields. In contrast, the constraint effective potential does not suffer from this infrared problem, and it can therefore be computed using perturbation theory. We discuss the physical interpretation of the two effective potentials. In particular, we provide evidence supporting an earlier conjecture that the constraint effective potential is the correct one to use in the stochastic Starobinsky-Yokoyama theory.

We study the quantum field theory of zero-temperature perfect fluids. Such systems are defined by quantizing a classical field theory of scalar fields ${\varphi }^I$ that act as Lagrange coordinates on an internal spatial manifold of fluid configurations. Invariance under volume-preserving diffeomorphisms acting on these scalars implies that the long-wavelength spectrum contains vortex (transverse modes) with an exact ${\omega }_T=0$ dispersion relation. As a consequence, physically interpreting the results obtained via perturbative quantization of this theory has proven to be challenging. In this paper, we show that correlators evaluated in a class of semiclassical (Gaussian) initial states prepared at $t=0$ are well defined and accessible via perturbation theory. The width of the initial state effectively acts as an infrared regulator without explicitly breaking diffeomorphism invariance of the classical action. As an application, we compute the stress tensor two-point correlators and show that vortex modes give a nontrivial contribution to the response function, nonlocal in both space and time.

We study the energy-momentum tensor of a dark matter (DM) spike formed during the adiabatic growth of a black hole embedded in a DM halo, and investigate its backreaction on the spacetime geometry. Within the Einstein cluster framework, we derive the complete tensor, explicitly incorporating the kinetic contribution to the energy density and the anisotropic pressure arising from noncircular particle orbits. Adopting the Hernquist profile as an illustrative model of DM halo and employing parameters appropriate to the Milky Way, we find that near the spike, the kinetic term enhances the total energy density by approximately 50% relative to the rest-mass component, while the nonzero radial pressure induces a mild anisotropy in the stress tensor. The derived tensor satisfies all standard energy conditions. By treating it as a fixed source in Einstein’s equations, we numerically obtain a static, spherically symmetric metric that deviates from the Schwarzschild solution by an amount more than twice that found when only the mass density is considered. These results demonstrate that including the full dynamical structure of the DM spike is essential for accurately modeling the backreaction of DM on black hole spacetimes.

We construct static, spherically symmetric black hole solutions in quasitopological gravity (QTG) coupled to Born-Infeld nonlinear electrodynamics. Starting from the spherically reduced action, we derive closed-form expressions for the electric field, the nonlinear Lagrangian, and the metric function, the latter involving hypergeometric functions. We consider specific versions of QTG in which vacuum black holes are regular, and show that, for some of these models, charged black holes develop a curvature singularity at a finite radius in their interior. In contrast, in models such as a Born-Infeld-type QTG, charged black holes remain regular. In this case, however, the de Sitter core of the neutral solution is replaced by an anti–de Sitter core. We also discuss several limiting regimes of these solutions.

Testing general relativity in the strong-field and highly dynamical regime is now possible through current gravitational-wave observations, where even a single high-quality detection can place competitive constraints on deviations from Einstein’s theory. The parametrized post-Einsteinian framework provides a theory-agnostic approach to search for such deviations, but it typically assumes that systematic uncertainties in the base waveform model, particularly those arising from calibration to numerical relativity, are negligible. In this work, we investigate how calibration errors in the late-inspiral fitting coefficients of the IMRPhenomD waveform model can lead to spurious detections of departures from general relativity in parametrized tests. We use an uncertainty-aware version of IMRPhenomD, recalibrated to a set of numerical relativity surrogate waveforms and equipped with a probabilistic description of its fitting coefficients, to simulate general-relativity-consistent signals. We inject these signals into an O5 ground-based detector network and recover them with the original IMRPhenomD model augmented with a parametrized post-Einsteinian phase deformation. We find that false violations of general relativity using this model arise for network signal-to-noise ratios as low as 60. When the uncertainty-aware model is used instead, the inferred parametrized post-Einsteinian phase deformation remains consistent with zero even for signals with a signal-to-noise ratio up to 330. These results demonstrate the need to account for numerical relativity calibration uncertainty in order to perform reliable inspiral tests of general relativity. They also illustrate that explicitly incorporating numerical relativity calibration uncertainty into the waveform model preserves our ability to robustly test general relativity.

Total transmission modes (TTMs) are modes with complex frequencies that propagate across a black hole spacetime without reflection. Recently, it is found that suitably tailored time-dependent scattering can excite these complex modes and suppress the reflected signal for the entire duration of the process, a phenomenon referred to as virtual absorption. Motivated by this, we present a study of the spectrum stability of TTMs using pseudospectrum and condition numbers. We focus on perturbations of $d$-dimensional Tangherlini black holes and recast the TTM problem as a generalized eigenvalue problem by utilizing the Eddington-Finkelstein coordinates. The results show that TTMs are generically spectrally unstable, with sensitivity increasing for higher overtones, in close analogy with quasinormal modes. A notable exception is the purely imaginary TTM in the positive imaginary axis in higher dimensions. Its pseudospectrum contours are nearly concentric, and its condition number is orders of magnitude smaller than those of the overtones, indicating enhanced spectral stability. As the spacetime dimension decreases, the condition number grows and becomes much larger in four dimensions in both the energy norm and the $L^2$ norm, suggesting possible spectral instability, although a definitive cross-dimensional conclusion is limited by the lack of a uniform physically preferred norm. Additionally, we confirm that purely imaginary TTMs occur for gravitational vector perturbations, whereas genuinely complex TTM families appear only in sufficiently high dimensions, $d\ge 8$, extending earlier claims that placed the onset at $d\ge 10$.

Future space-based gravitational wave (GW) observatories such as LISA will detect massive black hole binaries (MBHBs), which are expected to be accompanied by electromagnetic counterparts, thereby providing bright standard sirens for cosmology. The orbital eccentricity of MBHBs can significantly improve the parameter estimation of GWs because the multiple harmonics induced by eccentricity provide additional information and help break down the degeneracies among waveform parameters. In this paper, we use the EccentricFD waveform and construct 5-year GW event catalogs for LISA under three population models (PopIII, Q3d, and Q3nod). For the three models, we find that an initial eccentricity of $e_0=0.4$ at ${10}^{-4}\mathrm{Hz}$ yields improvements in sky localization and distance inference by a factor of $\mathcal{O}(10)$ in the best cases. As a consequence, the average number of bright siren candidates increases substantially: from 8 to 11 (PopIII), 6 to 12 (Q3d), and 13 to 24 (Q3nod). This increase in event number, together with enhanced localization and distance inference, leads to tighter cosmological constraints. In the $\mathrm{\Lambda }\mathrm{CDM}$ model, for instance, the relative uncertainty on $H_0$ is reduced from 8.17% to 4.35% for the Q3d model, corresponding to an improvement of approximately 47%. We also investigate the improvement in constraints on the dark energy equation of state and modified GW propagation when combining bright sirens with the latest cosmic microwave background data. These results demonstrate that eccentricity is a remarkably significant feature in GW detection and parameter estimation, enabling more accurate measurements of the Universe with future space-based observatories.

Regular black holes, free of central singularities, provide an ideal laboratory for probing the geometric structure of spacetime. The global structure of some regular black holes, e.g., Hayward black hole, features an event horizon and a Cauchy horizon, raising fundamental questions about the latter’s stability. In this work, we investigate the collapse of a scalar field in Hayward spacetime. Under weak scalar perturbations, the inner horizon maintains a stable finite radius. In the circumstance of a strong scalar field, the inner horizon shrinks to zero volume, accompanied by the formation of a spacelike singularity. The Hayward geometry is effectively converted into a Schwarzschild-like geometry. Furthermore, the characteristic parameter of the scalar field governs the contraction dynamics of the inner horizon. As the parameter $p$ of the initial profile for the scalar field approaches the critical threshold $p_{*}$, the radius of the inner horizon $r_{-}$ exhibits a universal scaling behavior: $r_{-}\propto |p-p_{*}{|}^{\gamma }$, with a critical exponent $\gamma \approx 0.5$.

Astrophysical black holes are invariably embedded in matter environments whose gravitational influence can alter key strong-field features of the spacetime. In this work, we investigate the impact of spherically symmetric dark-matter distributions on black hole geometry, geodesic structure, and ringdown phenomenology. Modeling the surrounding matter through Einstein clusters, we construct self-consistent spacetimes for three widely used density profiles—the Hernquist, Navarro-Frenk-White, and Jaffe models—and examine how their near-horizon behavior modifies the location and stability of circular timelike and null geodesics, including the innermost stable circular orbit (ISCO) and light rings. In the low-compactness regime, we derive analytical expressions showing that environmental effects generically shift the ISCO inward and the principal light ring outward, leading to parametric deviations in their associated orbital frequencies and Lyapunov exponents. At higher compactness, we explore the emergence of additional light rings, marginally stable orbits, and secondary horizons, identifying the regions of parameter space in which these additional geodesic structures arise. We introduce a perturbative approach to find approximate analytical solutions to the spacetime metric that are valid in astrophysical scenarios and compare them with the numerical solutions. Using time-domain evolutions of scalar perturbations, we demonstrate how such structures can imprint characteristic signatures on the ringdown signal, including long-lived trapped modes and echolike modulations associated with multiple potential barriers. Our results provide a unified framework for assessing environmental effects around black holes and highlight the importance of matter-induced corrections for interpreting upcoming electromagnetic and gravitational-wave observations.

Within the framework of scalar-tensor theories of gravity, certain models can evade classical black hole no-hair theorems. A well-known example is Einstein-scalar-Gauss-Bonnet gravity, where black holes carrying a scalar charge can exist. We find that, within this theory, binary black holes initially described by general relativity can acquire scalar charges once they reach a critical orbital separation (“dynamical scalarization”). We develop a simple semianalytic model, based on the adiabatic conservation of the total Wald entropy, to estimate the scalar charge evolution during the binary inspiral. We also run fully nonlinear numerical-relativity simulations for different configurations, finding consistent results. The gravitational-wave phase difference between Einstein-scalar-Gauss-Bonnet and general relativity waveforms, which we use to assess detectability, is also computed. We find that dynamical scalarization might be observable in nearly equal-mass binary black hole mergers with third-generation ground-based gravitational-wave detectors, in a narrow range of the dimensional coupling of the theory.

We investigate the motion of spinning test particles in the spacetime of a global monopole in the framework of the Mathisson-Papapetrou-Dixon equations. By making use of the symmetries of the spacetime, we obtain a general exact solution to the equations of motion. We show that the particle’s trajectories, momenta, and spin can be expressed in terms of three specific functions of the polar and azimuthal angles. We also show that the system is completely integrable. We obtain the general nongeodesic trajectory of the particle, and also examine the particular cases of radial and planar motion. We compare the nongeodesic trajectories of a spinning particle with a nonspinning particle.

We revisit the cosmic microwave background (CMB) constraints on the spatial curvature of the Universe, assessing how they change when the curvature parameter and the primordial inflationary scalar spectrum are treated consistently within theoretically motivated frameworks. Instead of relying on the phenomenological parametrization commonly used to capture curvature effects at the largest scales, we present a case study based on closed quadratic inflation, where the primordial spectrum is derived in full generality and in a gauge-invariant manner. Within this framework, we analyze both the plik public release 3 (PR3) and camspec PR4 Planck CMB likelihoods and find that the constraints on ${\mathrm{\Omega }}_{\mathcal{K}}$ shift toward spatial flatness. In plik the preference for ${\mathrm{\Omega }}_{\mathcal{K}}<0$ decreases from $\gtrsim 3.5\sigma$ to $\sim 2.5\sigma$, while in camspec it reduces further to $\sim 2\sigma$. At large angular scales ($\ell <10$), our model explains the low-$\ell$ power suppression anomaly, notably improving the fit to the quadrupole. However, the reduced preference for highly negative values of ${\mathrm{\Omega }}_{\mathcal{K}}$ only partially accounts for the lensing anomaly at high multipoles, worsening the fit to the plik spectrum at small scales. By contrast, in the camspec PR4 spectrum, where the lensing anomaly is less pronounced, the model yields an overall improvement. Our analysis highlights a key conceptual point: closed-inflation models tie the curvature parameter to the inflationary dynamics and the primordial spectrum, enforcing consistency conditions that do not necessarily allow for the large deviations from flatness seen in phenomenological parametrizations. In the case of quadratic inflation, these restrictions reduce the apparent evidence for negative curvature reported by earlier analyses, while allowing for a mildly closed geometry.

Recent cosmological data, including DESI DR2, highlight significant tensions within the $\mathrm{\Lambda }\mathrm{CDM}$ paradigm. When analyzed in the context of general relativity (GR), the latest DESI data favor a dynamical dark energy (DDE) equation of state, $w(z)$, that crosses the phantom divide line $w=-1$. However, this framework prefers a lower Hubble constant, $H_0$, than Planck 2018, thereby worsening the tension with local measurements. This phantom crossing is a key feature that cannot be achieved by minimally coupled scalar fields (quintessence) within GR. This suggests the need for a new degree of freedom that can simultaneously: (A) increase the best-fit value of $H_0$ in the context of the DESI DR2 data, and (B) allow the crossing of the $w=-1$ line within a new theoretical approach. We argue that both of these goals may be achieved in the context of modified gravity (MG), and in particular, scalar-tensor (ST) theories, where phantom crossing is a natural and viable feature. We demonstrate these facts by analyzing a joint dataset including DESI DR2, Pantheon+, CMB, and growth-rate (RSD) data in the context of simple parametrizations for the effective gravitational constant, ${\mu }_G(z)\equiv G_{\mathrm{eff}}/G_N$, and the DDE equation of state, $w(z)$. This MG framework significantly alleviates the tension, leading to a higher inferred value of $H_0=70.6\pm 1.4\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1}$. We also present a systematic, data-driven reconstruction of the required underlying ST Lagrangian and provide simple, generic analytical expressions for both the nonminimal coupling $F(\mathrm{\Phi })=1+\xi {\mathrm{\Phi }}^2{e}^{n\mathrm{\Phi }}$ and the scalar potential $U(\mathrm{\Phi })=U_0+a{e}^{b{\mathrm{\Phi }}^2}$, which well describe the reconstructed functions.

Cosmic voids, the underdense regions of the large-scale structure, provide cosmological information highly complementary to that obtained from overdense regions. In this work, we investigate the constraining power of the void-shear cross-correlation (void lensing effect) on the total neutrino mass. Based on cosmological $N$-body simulations with varying neutrino masses, we populate BOSS LOWZ-like galaxies at $0.2<z<0.4$ using halo occupation distribution fitting, identify voids with the dive void finder, and obtain their density profiles from the underlying dark matter and neutrino distributions. We then generate mock shear catalogs through ray tracing and measure the corresponding void lensing signals, assuming a source number density of $10/{\mathrm{arcmin}}^2$ and sky area of around $8400{\mathrm{deg}}^2$. Under this setup, void lensing independently yields a constraint on total neutrino mass as $\sigma (M_{\nu })=0.096\mathrm{eV}$ [$M_{\nu }<0.232\mathrm{eV}$, 95% confidence level (CL)] in the absence of shape noise, and $\sigma (M_{\nu })=0.340\mathrm{eV}$ ($M_{\nu }<0.707\mathrm{eV}$, 95% CL) when adopting a stage-III-like shape noise. Moreover, we find a clear linear relationship between the void lensing signal and neutrino mass. We further validate the forward modeling of the void lensing signal from the void density profiles across different cosmologies, demonstrating its accuracy and potential for future applications. These findings highlight void lensing as a promising probe of massive neutrinos and motivate its applications to galaxy survey data as well as the combination with other cosmological observables.

We present a comprehensive investigation of the $\mathcal{F}\text{−}\mathrm{statistic}$ method for parameter estimation of gravitational wave (GW) signals from compact binary coalescences. By analytically maximizing the likelihood over the luminosity distance and polarization angle, this approach reduces the dimensionality of the parameter space to enhance computational efficiency. We also introduce a novel formulation for calculating the Bayesian evidence for the $\mathcal{F}\text{−}\mathrm{statistic}$, enabling a quantitative assessment of its performance against standard full frequency-domain (FFD) Bayesian inference. Applying these two methods to analyze several representative GW events (GW190412, GW190814, and GW170817), we find that the $\mathcal{F}\text{−}\mathrm{statistic}$ consistently yields results in good agreement with the FFD approach, while offering a significant reduction in computational cost. We demonstrate that including calibration uncertainty generally improves the agreement between the two methods. Furthermore, under the assumption of physical priors, the $\mathcal{F}\text{−}\mathrm{statistic}$-based analyses consistently yield higher Bayesian evidence than the corresponding FFD analyses. While the $\mathcal{F}\text{−}\mathrm{statistic}$ produces slightly broader constraints on some parameters, we argue this represents a more honest uncertainty quantification, particularly in high-dimensional parameter spaces with complex posterior structures. These results highlight the significant advantages of the $\mathcal{F}\text{−}\mathrm{statistic}$ method for GW data analysis, positioning it as a powerful tool for the era of high-rate detections with future observatories.

The gravitational wave $\omega$ mode spectrum presents a unique window into the dense interior of neutron stars, probing physics inaccessible to electromagnetic observations. This work investigates the $\omega$ modes of compact stars composed of quarkyonic matter. The quarkyonic model, which describes a crossover transition between nucleonic and quark matter treated as quasiparticles, is formulated within the relativistic mean-field (RMF) theory using the G3 and IOPB-I parametrizations. This core is surrounded by a mantle of hadronic matter, creating a multicomponent stellar interior. The overall equation of state (EOS) is governed by two key parameters: the transition density ($n_t$), and the QCD confinement scale (${\mathrm{\Lambda }}_{\mathrm{cs}}$), which are varied to construct models consistent with current astrophysical constraints on mass and radius. We compute the complex eigenfrequencies (damped oscillations) of the fundamental and first excited $\omega$ modes using the phase-amplitude method within a full general relativistic framework. Our simulations reveal that the admixed quarkyonic structure produces a unique $\omega$ mode signature, distinctly different from pure hadronic or hybrid stars. The spectrum exhibits a strong, degenerate dependence on the EOS, where the stiffening effect of the quarkyonic matter influences oscillation frequencies and damping times in a characteristic manner. We also demonstrate that $\omega$ mode frequencies for quarkyonic stars follow approximate universal relations, largely independent of the EOS.

A system of classical interacting spins can develop collective instabilities, which, in the nonlinear regime, mimic the motion of a gyroscopic pendulum. Known as the flavor pendulum, this behavior appears among the collective modes of a dense neutrino plasma after a strong reduction of phase space through symmetry assumptions. It has been identified in homogeneous slow and fast flavor systems and, most recently, in single-wave solutions of the fast system. For the first time, we explain the reasons for its ubiquitous appearance. We show that a system of three classical spins must always be pendular, or only two in the presence of an external field. Furthermore, such a system always defines a continuum of vectors with time-independent length. If these are identified as interacting spins, they immediately lead to the continuum cases of slow and fast flavor pendula. As another new insight, any of these spins can be chosen as the pendulum, periodically exchanging flavor with the rest of the system.

Gravitational wave (GW) observatories have used template-based search to detect hundreds of compact binary coalescences (CBCs). However, template-based search cannot detect astrophysical sources that lack accurate, computationally tractable waveform models. Here, we present a novel approach for template-free search using coincident anomaly detection (CoAD). CoAD requires neither labeled training examples nor background-only training sets, instead exploiting the coincidence of events across spatially separated detectors as the training loss itself: two neural networks independently analyze data from each detector and are trained to maximize coincident predictions. Additionally, we show that integrated gradient analysis can localize GW signals from the neural network weights, providing a path toward data-driven template construction of unmodeled sources and further improving precision by frequency matching. Using the Codabench dataset of real LIGO backgrounds with injected simulated CBCs and sine-Gaussian low-frequency bursts, CoAD achieves recall up to 0.91 and 0.85, respectively, at a false-alarm rate of one event per year and achieves recall above 0.5 at signal-to-noise ratios below 10. The fully unsupervised nature of CoAD makes it especially well suited for next-generation detectors with greater sensitivity and associated increases in GW event rates.

In this work, we present a novel and more efficient approach to constructing the relativistic Bobylev, Krook, and Wu (BKW) solution [A. V. Bobylev, Sov. Phys. Dokl. 20, 820 (1976).; M. Krook and T. T. Wu, Phys. Fluids 20, 1589 (1977).] of the relativistic Boltzmann equation. Introducing a new ansatz for the distribution function, we demonstrate that within this specific ansatz space, only the equilibrium and BKW-type forms yield exact solutions to the nonlinear Boltzmann equation. Furthermore, we also derive the Lie algebra of invariant transformations admitted by the relativistic Boltzmann equation and show that the corresponding symmetry group transformations can be systematically constructed from this algebra.