Papers

We examine the dipole structure in the local cosmic expansion rate $H_0$ using the Pantheon+ compilation of Type Ia supernovae. We reconstruct directional maps of $H_0$ across the sky within the low-redshift regime, $z_{\rm min} < z < 0.2$, evaluated in the CMB rest frame. To perform a tomographic analysis, we choose 10 different values for $z_{\rm min}\in [0.015 , 0.045]$ range. We find a dipole amplitude $A_{\rm dip}=1.16\pm0.28\ {\rm km/s/Mpc}$ for the lowest bin, monotonically decreasing to $A_{\rm dip} =0.35\pm0.52\ {\rm km/s/Mpc}$, as we increase $z_{\rm min}$. Since $A_{\rm dip}$ is positive-definite, by construction $A_{\rm dip} > 0$ even in an isotropic universe, thus to assess the statistical significance, we compare to $A_{\rm dip}$ generated from 1000 Monte Carlo simulations based on the $\Lambda$CDM model and the same redshift ranges. Our results reveal a $2-3\sigma$ dipole pattern (depending on how the significance level is computed) for $z_{\rm min}\lesssim 0.032$. For redshift thresholds where the signal remains statistically significant ($>2\sigma$), the inferred dipole direction points close to Shapley supercluster and CMB dipole directions. As $z_{\rm min}$ increases, the dipole amplitude diminishes in line with expectations of a higher redshift isotropic Universe, but the difference in maximal antipodal $H_0$ determinations, $\Delta\text{H}_0^{\rm max}$, retain a signal of an anisotropy that disappears in the dipole ansatz. The decreasing statistical significance of all estimators with increasing $z_{\rm min}$ suggests that any $H_0$ dipole is a low-redshift feature.

We investigate the semiclassical Hawking evaporation of a two-dimensional Callan-Giddings-Harvey-Strominger (CGHS) black hole perturbed by first-order Horndeski scalar-tensor couplings. By evaluating the exact scalar curvature invariants, we demonstrate that coordinate singularities near the apparent horizon parametrize a physical deformation of the surface gravity while preserving a strictly regular event horizon. In the linear-order $\gamma_3 \Phi X$ coupling sector, the surface gravity and correspondingly the Hawking temperature decreases dynamically as the black hole loses mass. Extrapolating this cooling effect via a resummed temperature equation suggests that evaporation halts, potentially leaving behind a stable, macroscopic cold remnant at the boundary of perturbative control. Utilizing both the conformal trace anomaly and the Robinson-Wilczek gravitational anomaly, we establish that the asymptotic radiation flux identically reflects this geometric shift. Consequently, the fine-grained entanglement entropy of the Hawking radiation departs from linear growth and transitions to an asymptotic logarithmic regime. This indicates that quantum information may be permanently retained within the remnant, altering the standard semiclassical Page curve without requiring a breakdown of horizon regularity.

Unlike the neutron-star mass–radius relation, which depends sensitively on the internal stellar structure through the equation of state of dense nuclear matter, certain neutron-star properties obey approximately universal relations that exhibit only weak dependence on the equation of state. In this paper, we explore new universal relations for magnetized neutron stars. We focus on a purely poloidal dipolar magnetic-field configuration and treat the effects of the magnetic field perturbatively to second order in the field strength. After appropriately normalizing the relevant quantities by the stellar mass and the magnetic-field strength at the pole, we first identify an exact universal relation between the magnetic dipole moment and stellar compactness. We then find approximate universal relations among the magnetic dipole moment, magnetically-induced stellar quadrupole moment, and ellipticity, with fractional variations due to the equation of state at the level of O(10%). We support these numerical findings with analytic estimates for Newtonian polytropes, which reproduce the observed behavior. Among the newly discovered relations, the one connecting the magnetic dipole moment and stellar quadrupole moment may be particularly useful for the analysis of gravitational-wave signals from binaries containing magnetized neutron stars.

In the context of quantum cosmology, we study quantum entanglement in solutions of the Wheeler–DeWitt equation for a homogeneous inflaton–gravity system coupled to perturbations. The wave function describing the homogeneous degrees of freedom is entangled with the wave function describing the perturbations, and this may lead to potentially observable effects on the inflationary spectra. We restrict our analysis to two simplified models that admit a future de Sitter attractor, while neglecting non-adiabatic effects and contributions of order $\mathcal{O}(\hbar^2)$ in the Mukhanov–Sasaki equation. Analytical expressions for the resulting spectra are obtained by marginalising over the homogeneous inflaton variable and can be evaluated in regimes where reliable approximations are available. Small deviations from the standard semiclassical spectra are indeed generated, and these are significantly larger than the quantum-gravitational corrections usually considered in this context.

We construct static, spherically symmetric, and asymptotically flat colored black holes in four-dimensional Einstein gravity coupled to a logarithmic nonlinear Yang–Mills field with gauge group SU(2). Unlike solutions based on the Wu–Yang ansatz, the gauge sector contains a dynamical radial amplitude, and the configurations arise from a genuinely coupled nonlinear boundary-value problem. An integral identity excludes nontrivial sign-definite solutions approaching a magnetically neutral Yang–Mills vacuum, implying that colored configurations must be nodal. We numerically construct the fundamental one-node branch and verify its convergence to the ordinary Einstein–Yang–Mills colored black hole in the linear limit. Increasing the logarithmic nonlinearity lowers the ADM mass, raises the Hawking temperature, and displaces the gauge-field node toward larger radii. Branch termination is not detected over the full range of parameters investigated. Instead, the exterior geometry approaches Schwarzschild on fixed radial domains, while the colored structure develops an increasingly extended tail. Although no independent asymptotic Yang–Mills charge is present, the non-Abelian hair leaves a subleading imprint on the far-field geometry. Inside the event horizon, the representative nonlinear solutions possess no Cauchy horizon and approach a Schwarzschild-type spacelike curvature singularity, with a finite limiting mass and no oscillary mass inflation. The recovery of the linear theory is therefore nonuniform near the cetonter: solutions that are nearly linear in the exterior eventually enter the strongly logarithmic regime in the deep interior. Finally, turning points of the Hawking temperature produce divergences and sign changes in heat capacity, indicating transitions of local thermodynamic stability.

Neutrinos can acquire electromagnetic moments either within the Standard Model through higher order radiative corrections or within the domain of new physics. In this study we focus on probing these beyond the standard model neutrino moments through quenched superradiance of black holes where fermionic pairs can be produced from the superradiant bosonic cloud. We consider the production of dark photons from black hole superradiance and quenching occurs through the production of neutrino-antineutrino pairs from the dark photons. The efficiency of the pair production depends on the effective coupling between the dark photons and neutrinos, i.e., the dark electromagnetic moments. We also discuss bounds on primordial black hole abundance from neutrino background arising from this quenched superradiance mechanism.

Pulsar timing arrays (PTAs) have detected a stochastic gravitational-wave background (SGWB) in the nanohertz band, enabling tests of gravity and cosmology, as well as studies of supermassive black holes and early Universe physics. PTA data analysis relies on cross-correlating timing residuals, where overlap reduction functions (ORFs) critically determine sensitivity. Conventional ORF calculations using the short-wavelength approximation break down for the scalar longitudinal mode and cannot handle frequency dependence or anisotropies. This work rigorously derives the full response functions within an analytical cross-correlation framework. We reveal, for the first time, intrinsic symmetries and relations among anisotropic ORF integrals for all polarizations. By variable substitutions and coordinate rotations, we transform complex integrals into tractable forms, resolving divergences in vector and scalar longitudinal modes. Building on this, we establish a universal framework yielding fully analytical expressions for anisotropic ORFs to arbitrary order for all six modes. As a direct application, we give complete expressions up to l <= 5. This framework is free of approximations; its (0,0) component recovers the isotropic Hellings–Downs curve. Compared with numerical integration, our results offer broader applicability, faster computation, and higher precision, providing a valuable foundation for anisotropic sky mapping, polarization-mode separation, and new-physics searches with PTA data.

We develop an operator formulation of the entropy-geometry correspondence for static, spherically symmetric gravity. Starting from a generalized entropy, we reconstruct an effective nonlocal form factor, its coordinate-space source, the associated cumulative mass profile, and the resulting spacetime geometry. The construction is worked out for the Bekenstein-Hawking, Rényi, Tsallis-Cirto, Barrow, Kaniadakis entropies, logarithmically/exponentially corrected entropy and LQG inspired entropy. The operator representation provides a direct relation between generalized entropy, nonlocal gravitational dressing, and a scale-dependent effective mass or Newton coupling. We analyze the reconstructed sources and their infrared and ultraviolet behavior, discuss their physical consistency, and identify the limits in which the standard Schwarzschild description is recovered. We show that the generalized entropy exactly reproduces the area law with the reconstructed running Newton coupling, $\dd S=\dd A/4G_S(r_+)$, ensuring thermodynamic consistency. Since horizon entropy is determined by the action, this favors entropy corrections in the gravitational sector. We also derive the conditions for the reconstructed horizon to be an event horizon with positive temperature.

With the arrival of advanced telescopes such as the Event Horizon Telescope (EHT), direct imaging of a black hole's shadow became a reality. Simulations play an important role in reproducing their appearance and constraining physical parameters of the black hole. We present a simple framework of simulating images of Schwarzschild black holes surrounded by thin, rotating accretion disks, accounting for gravitational and Doppler redshifts. A ray tracing algorithm based on integrating the photon geodesic equations with a 4th-order Runge-Kutta scheme is used for imaging. The accuracy of the numerical method is verified by convergence tests. A brief discussion of the validity of the weak field approximation is included and a qualitative comparison between the simulated images and the EHT image of M87* is presented.

We present the first joint cosmological analysis to extract both geometric and dynamical information from galaxy intrinsic alignments (IAs). Using BOSS spectroscopy cross-matched with galaxy shape measurements from the DESI Legacy Imaging Surveys, we measure anisotropic galaxy density–intrinsic ellipticity (GI) and intrinsic ellipticity (II) correlations over $0.43\leq z\leq0.7$ and decompose their spin-dependent angular structure into associated Legendre multipoles. The measured GI correlation exhibits the expected baryon acoustic oscillation (BAO) structure, while its anisotropy provides geometric information complementary to galaxy clustering. By jointly modeling redshift-space and Alcock-Paczynski distortions, we constrain the growth rate parameter $f\sigma_8$, the angular-diameter distance $D_A$, and the Hubble expansion rate $H$. Relative to galaxy clustering alone, adding IA reduces their fractional uncertainties by 32%, 18%, and 29%, respectively. By mapping these constraints onto a flat $w_0$CDM model, IA also tightens the constraints on $w_0$, $\Omega_m$, and $H_0$; however, the $w_0$ constraint is sensitive to the minimum scale included in the analysis. Our results establish anisotropic galaxy shapes as an additional source of geometric and dynamical information for spectroscopic cosmology.

The event horizon telescope (EHT) has opened a new window onto the strong-field regime by imaging the shadows of the supermassive black holes (SMBHs) Sgr A* and M87*. These observations provide a unique laboratory for probing the dark matter (DM) distribution around black holes. In this work we systematically investigate the imprints of two distinct DM halo models, the cold DM (CDM), and the cored scalar field DM (SFDM) profiles on the gravitational lensing signatures of Sgr A* and M87*. We compute the photon spheres, shadows, weak and strong lensing observables, and caustic structures for both models. We then compared the obtained values of the shadow diameters with the EHT data, using $\chi^2$ statistics. We found that all the models are within $1.2\sigma$ of the measured shadow diameters with the small $\chi^2$ differences, $\Delta\chi^2 \lesssim 1.2$. The caustic analysis reveals distinct topological regimes, Sgr A* retains both tangential and radial critical curves, while M87* may show only tangential critical curves due to its larger mass. This topological difference provides a clear observational signature for future observations.

We study the $U(1)^4$ charged black brane solution of four-dimensional gauged supergravity and analyze the fermionic response in this geometry, which is holographically dual to $3d$ $\mathcal{N}=2$ SCFT ABJM models. Similar to \cite{DeWolfe:2013fha}, we show that a gap exists in the states of the conformal field theory, which corresponds to the different limiting behaviors of the two unequal chemical potentials of the four-charge geometry. We study the behavior of this gap and also the stability of the near-horizon geometry by changing the parameters of the theory in various orders. We then categorize the $56$ fermion modes of the geometry, find the coefficients of the Dirac equations for each mode, and comment on the behavior of the solution of the Dirac equation in different near-horizon limits. We then uplift the geometry to five-dimensional and then to eleven-dimensional geometries and, similar to \cite{Fareghbal:2008dy}, we show that in both cases, a piece of $\mathrm{BTZ} \times \mathrm{S}^2$ or $\mathrm{AdS}^3 \times \mathbb{R}^2$ emerges, and as a result, a decoupling sector in the field theory exists. We study the singularity of the near-horizon $4d$ geometry and the mentioned gap in these uplifted geometries.

We demonstrate that a Bianchi-I spacetime in general relativity must be geodesically past-incomplete under the assumption of the null energy condition and provided there exists a time in which the universe is expanding in all directions. Spacetimes which are always contracting along at least one direction are not subject to the conclusion, and we provide an explicit example. A distinguishing feature of our theorem is that it makes no assumption on the global topology of the spacetime.

It has been shown that the spectrum of black hole quasi-normal modes is extremely sensitive to localized deformations of the geometry away from the potential peak. The deformation caused by a real astronomical environment will extend throughout the whole space rather than be localized in a finite region. Whether spatially extended fluctuations distributed throughout spacetime can produce similar effects remains unclear. In this work, we construct a toy model to investigate the case that the deformation of the metric is not localized but extends throughout the whole space. We study how it changes the ringdown stage of the black hole in the time domain. Using both the Pöschl-Teller and Regge-Wheeler potentials as representative backgrounds, we show that sufficiently wide spatially periodic perturbations of zero mean can trigger not only the “spectral instability” in the frequency domain but also black hole instabilities in the time domain. Through numerical analysis, we uncover a universal scaling relation for the instability threshold and further provide an analytical interpretation of its physical origin.

Primordial black holes (PBHs) formed in the early Universe remain a viable dark matter candidate. Since dark matter is expected to be concentrated toward galactic centres, a significant population of PBHs would reside near a supermassive black hole (SMBH), providing a promising environment for gravitational wave emission. We consider PBHs with masses from $10^{-15}$ to $10$ solar masses on hyperbolic trajectories past an SMBH, that produce bursts of gravitational radiation during periastron passage. Sagittarius A* is an obvious location for these events, but we show that both M31* and M87* would generate similar signals, albeit at lower frequencies. We assess the detectability of both individual bursts and "popcorn" backgrounds, relative to LISA and the proposed $\mu$Ares mission. Comparing these results to plausible central halo densities, we find that unbound PBHs are unlikely to yield detectable signals.

We construct a nonlinear electrodynamics (NLED) model for a static magnetic black hole. Rather than imposing a regular center, we require a Maxwell weak-field limit, finite magnetic self-energy, a positive and subluminal electromagnetic cone, the standard energy conditions, and a static exterior that satisfies known sufficient stability criteria. A positive mixture of power kernels restricts the exponent to $1/4<\gamma\leq1/2$. For the minimal two-kernel model, with $\gamma_1=1/3$ and $\gamma_2=1/2$, the field equations admit an exact solution in terms of incomplete beta functions. For the branches with nonnegative Schwarzschild mass parameter $M_0$, the metric function is strictly increasing, so there is at most one positive-radius horizon and no inner Cauchy horizon. We construct the maximal extension and show that the black-hole, horizonless, and critical branches have spacelike, timelike, and null singularities, respectively. The representative black-hole families have positive temperature and negative fixed-charge heat capacity. Electromagnetic waves split into ordinary and extraordinary optical branches. We calculate their photon spheres, shadow radii, instability rates, and illustrative Event Horizon Telescope size bands. We also construct ISCO-truncated thin-disk images. The full images remain close, but jointly normalized residual maps and radial profiles reveal a coherent branch-dependent shift near the lensed inner edge and the critical region. The extraordinary branch moves the critical curve outward and partly compensates the shadow reduction caused by magnetic charge.

GW231123 is an exceptional gravitational wave event for which different waveform models yield significantly different inferred source parameters. Residual tests provide a direct way to assess whether each waveform model gives an adequate description of the observed signal. In this work, we extend the conventional residual-test methods by subtracting the 100 highest likelihood waveforms, rather than only the maximum likelihood waveform for each model, thereby propagating waveform reconstruction uncertainty into the residual analysis. This ensemble-based approach turns the residual test from a single waveform diagnostic into a robustness test over the local high likelihood waveform manifold. We further perform injection tests to quantify the detectability of cross-model waveform discrepancies in realistic detector noise. The large-scale implementation of these analyses is made possible by the high speed and low computational cost of our residual testing framework, which is based on three goodness-of-fit tests: the Kolmogorov-Smirnov test, the Anderson-Darling test, and Pearson's chi-squared test.

We present an exact analytical model of axisymmetric gravitational collapse leading to the formation of the Kerr black hole. The model depends only on the total mass ${\cal M}$ and a time dependent rotation parameter $a(v)$, and incorporates both the extremal Kerr black hole and a novel quasi extremal regime without requiring $a\approx{\cal M}$. The evolution develops curvature singularities induced by $a(v)$, which are expected to remain enclosed within a trapped region close to the evolving Kerr radius $r=h(v)$. It also predicts a transient anisotropic exterior curvature decaying as $1/r^2$, which may imprint observable signatures associated with the formation of a rotating black hole. The present construction should therefore be interpreted as an exact analytical description of the final stage of rotational gravitational collapse, immediately preceding the formation of the Kerr black hole.

We consider the emission of gravitational waves (GW) from a compact binary in a spacetime with compactified extra dimensions. We solve the homogeneous and non-homogeneous wave equation, proving that there is an infinite sum of exponentially decaying pseudo-massive modes which add to the usual one which behaves as 1/r at infinity. We calculate the metric potentials, the equations of motion and the energy flux. We find that in the equations of motion there is a new term at -1PN order. This implies a modification of the energy flux.

Dark matter and dark energy could be ultra-light pseudoscalar fields that couple to electromagnetism through a Chern-Simons term. This would cause a parity-breaking rotation of the plane of linearly polarized light from the cosmic microwave background, known as cosmic birefringence, which is not predicted by $\Lambda$CDM. Recent hints of a non-zero cosmic birefringence angle have been found in both the Planck Data Release 4 and ACT Data Release 6 datasets independently. This work jointly analyzes the polarized maps of both, leveraging the cross-power spectra between the two telescopes. Taking the reported instrumental priors at face value, the joint analysis yields $\beta = 0.277^{\circ} \pm 0.057^{\circ}$, which is non-zero with a statistical significance of $4.8\sigma$. A robustness test mitigating contamination from dust emission excludes $\beta = 0^{\circ}$ at $3.5\sigma$, and retrieving $\beta=0^{\circ}$ would require both the dust $EB$ modeling and instrumental priors to fail simultaneously. However, unresolved systematics in the data must be understood before we can draw strong cosmological conclusions.

We study semiclassical geometries induced by turning on identical sinusoidal scalar sources on two asymptotic anti-de Sitter (AdS) boundaries. Varying the source strength, we find that large and small wormhole solutions appear beyond a certain threshold. Above this threshold, the large wormhole is always the dominant saddle in the two-boundary gravitational path integral; there is no regime where wormholes are subdominant. Under the ensemble interpretation of the gravitational path integral, this implies that once wormhole solutions exist, the putative ensemble has exponentially large fluctuations relative to the mean. This is unlike previously studied examples of wormholes sourced by inhomogeneous matter which have a region in parameter space where wormholes are subdominant, and therefore the ensemble is sharply concentrated around the mean. Interpreting the bulk geometries as holographic renormalization group (RG) flows, we also find that the sinusoidal modulation of scalar boundary sources results in effective holographic $\beta$-functions which are multivalued, indicating exotic RG flows. In particular, disconnected geometries correspond to flows that return to the starting fixed point in the infrared, while wormholes describe flows to a gapped phase in the infrared.

Rare fluctuations in physical systems depend on the detailed microphysics responsible for the fluctuations. In classical statistical systems, the large deviation principle has elucidated the role of semi-classics in describing this regime, and has simultaneously provided a the mathematical foundation of statistical mechanics. Large deviation theory for quantum system is considerably less developed. As all physical systems are fundamentally quantum mechanical, this leaves a major gap in our understanding of rare fluctuations relevant to statistical physics, cosmology, and more. In this paper, we develop the practical aspects of the theory of large deviations relevant for calculating rare events in physical systems from quantum walks to cosmology. We first analyze the case of the anharmonic oscillator coupled to a bath, showing explicitly how the system evolves from dominantly statistical (e.g. thermal) to quantum fluctuations. We then generalize these results, showing that the dominant rare fluctuations minimize the measurement-induced relative entropy. This perspective provides a thermodynamic description of a wide range of open quantum systems. We apply these results to random walks that arise in cosmology through stochastic inflation. We show that the evolution of the density matrix of long wavelength fields on a fixed de Sitter background breaks the KMS symmetry, giving rise to a stationary density matrix that does not respect detailed balance.

We investigate dark matter admixed neutron stars in which the neutron star coexists with an anisotropic dark matter halo described by the Einasto density profile, a model recently shown to produce regular, singularity-free black hole solutions~[Phys. Rev. D 113, 043011 (2026)]. Solving the modified Tolman–Oppenheimer–Volkoff equations with two different equations of state (BSk19 and SLy4), we find that the dark matter halo significantly alters the neutron star structure. Furthermore, for a specific range of halo parameters, $g_{rr}^{-1}$ changes sign outside the stellar surface, forming an event horizon with the neutron star persisting as a regular configuration inside it— “neutron stars in black holes”. This configuration appears in both equations of state and does not depend on a specific choice of the equation of state. The discovery of this configuration provides a new perspective and a concrete computable instance for the study of what lies inside a black hole.

We investigate the open quantum dynamics of a system of two masses interacting with an environment of linearized gravitational waves. We formulate the analysis in terms of the observable proper distance between the two masses, and show that the canonical variables obtained from the standard Lagrangian, expressed in terms of the Fermi normal coordinates, are not suitable for an effective description of the system. We resolve this issue through a unitary transformation that provides a physically meaningful system–environment decomposition and derive the master equation to leading order in $G$. Its dissipative sector reproduces the classical energy loss due to gravitational-wave emission, while the noisy contributions suppress coherences between states with different mass quadrupole, or effectively, different proper separations. In the regime where the proper distance can be described by considering small quantum fluctuations around an average distance $l_0$, the dynamics reduces to a Caldeira–Leggett-type equation, with a decoherence rate dependent on the baseline length $l_0$.

We investigate timelike particle dynamics, collision energetics, and photon frequency shifts in the perturbative variable-scalar curvature branch of asymptotically flat symmergent gravity. The low-energy vacuum action contains an $R^{2}$ correction whose coefficient is set by the boson–fermion imbalance of the underlying quantum field theory. At linear order, the exterior geometry is conformal to Schwarzschild spacetime through a radial mode satisfying a linear equation. We retain an independent boundary-condition-dependent amplitude and restrict the analysis to the perturbative domain. The two signs of the symmergent parameter $\gamma$ yield distinct profiles: $\gamma>0$ gives a Yukawa-suppressed deformation, whereas $\gamma<0$ produces an oscillatory inverse-radius deformation. We derive radial equations, effective potentials, circular-orbit and marginal-stability conditions for neutral, electrically charged, and spinning massive particles. Charged particles are treated in the test-field approximation, while spinning particles obey the Mathisson–Papapetrou–Dixon equations with the Tulczyjew condition. We also compute the center-of-mass energy of neutral-particle collisions and the frequency shifts of photons emitted tangentially by circular geodesic sources and detected by a static observer at infinity. The redshift and blueshift factors satisfy $(1+z_{+})(1+z_{-})=1/A(r_e)$, directly linking their product to the lapse function at emission. The $\gamma>0$ branch yields smooth, short-range deviations from Schwarzschild dynamics, whereas the $\gamma<0$ branch can generate oscillatory radial bands admitting circular-orbit solutions whose stability must be tested independently. These observables provide complementary probes of the variable-curvature sector, although their quantitative interpretation also depends on the deformation amplitude and, for the oscillatory branch, its phase.

We present a unified study of scalar, vector, and tensor quasinormal modes (QNMs) of Schwarzschild black holes corrected by a Gauss–Bonnet (GB) term in higher dimensions. Using a high-precision Chebyshev spectral method, we map the QNM spectra across $D\in\{5,6,7,8,10,11,12,26\}$ well beyond the regime where sixth-order WKB and characteristic-integration techniques remain reliable. Across the three spin sectors, we find several robust signatures of higher-curvature dynamics: the appearance of overdamped purely imaginary modes, non-monotonic behaviour in the real parts of higher overtones, and a strong amplification of the dimensionless QNM frequencies in string-motivated dimensions. In the scalar and vector sectors, we uncover an exact isospectrality between the scalar monopole ($\ell=0$) and vector dipole ($\ell=1$) at vanishing GB coupling, and we provide an analytic proof based on a Darboux factorisation of the corresponding Hamiltonians. In the tensor sector, we obtain the first numerical confirmation of the long-predicted instability in six dimensions; its onset is sharply captured by the Cohn–Calogero bound and leads to the mass threshold $GM\leq 158.1\,\alpha^{3/2}$. No analogous instability is found for $D\geq 7$, and no tensor isospectrality occurs. Converting the dimensionless frequencies to physical units suggests that the amplified modes in higher dimensions may enter the sensitivity window of future space-based detectors such as DECIGO. The merged analysis provides a comprehensive benchmark for QNMs in Einstein–Gauss–Bonnet gravity and highlights the limitations of standard approximation schemes in the strong-coupling and high-overtone regimes.

We propose a novel analytic approach to the study of multi-component FLRW cosmologies and their perturbations. The dynamics is triggered by a single scalar field with a scalar potential codifying the energy density and pressure of the multi-component fluid. This description unifies standard Big Bang cosmologies, models of inflation and dark energy under a unique framework. The key to integrability is to express the scalar potential in terms of the Hubble function $H(\phi)$ that plays the role of a fake superpotential, turning the dynamics into a first order problem, that may be analytically solved in a suitable time coordinate. In this framework, we propose integrable inflationary models with similar properties to the ones analysed in the literature and compatible with observations. Finally, we study scalar and tensor cosmological perturbations in each model by integrating Mukhanov-Sasaki equations via numerical and (semi-)analytic techniques. This allow us to compute the power spectrum, the spectral indices and the tensor-to-scalar ratio beyond the slow-roll approximation and compare our general results {against} the currently available observations and the theoretical predictions based on the slow-roll approximation.

We compute the lowest radial mode of spherically symmetric boson stars along equilibrium branches with a fixed number of radial nodes, considering both mini boson stars and quartically self-interacting models. By reformulating the pulsation equations in additive variables that remain regular at the zeros of the background scalar field, the eigenvalue problem can be integrated directly through the nodes of excited configurations. For all branches examined, the first zero of the constrained fundamental radial eigenvalue coincides, within numerical resolution, with the first simultaneous critical point of the Arnowitt–Deser–Misner (ADM) mass, Noether charge, and binding energy. We further evaluate the radial eigenvalue for the threshold models identified in nonlinear spherical evolutions of excited boson stars and find a simple empirical correlation with the node number and self-interaction strength. Our results provide a regular perturbative framework for excited boson stars and clarify the relation between constrained radial modes, equilibrium critical points, and nonlinear stability diagnostics.

We study static, spherically symmetric axion–dilaton solutions of the tree-level four-dimensional string effective action. Using the sigma-model structure of the scalar sector, we show that the full family of static, spherically symmetric and asymptotically flat solutions is obtained as the $SL(2,\mathbb R)$ orbit of the pure-dilaton FJNW solution, and we characterize the associated axion–dilaton charge space. We then analyze the perturbative regime of these solutions by comparing the onset of $\alpha'$ curvature corrections with that of string-loop corrections. Finally, we apply the string–black-hole correspondence criterion to the FJNW family by evaluating the local $\alpha'$ curvature diagnostic at the physical size $R_{\rm typ}$ of a highly excited string state. With the normalization fixed on the Schwarzschild branch, Schwarzschild saturates the nominal $\alpha'$ threshold at the correspondence surface, whereas every scalar-haired FJNW branch lies above it. More generally, independently of the common overall normalization within the matching prescription, every nonzero-hair branch has a larger curvature diagnostic at the correspondence surface than Schwarzschild. Away from the correspondence point, scalar-haired exteriors may remain under $\alpha'$ control at sufficiently weak local self-gravity and may provide perturbatively controlled long-distance fields of highly excited string states whenever the local string coupling also remains weak.

Extreme-mass-ratio inspirals (EMRIs) encode more than $10^5$ strong-field orbital cycles and are key targets for space-borne gravitational-wave interferometers, yet coherent recovery of generic systems over astrophysically broad priors remains unresolved. Successive Mock LISA, LISA, and Taiji Data Challenges (MLDCs, LDCs, and TDCs) have not yet produced a complete, generally reliable solution for blind EMRI detection and parameter recovery across such priors. The central obstacle is a needle-in-a-haystack likelihood: six phase-evolution parameters span a vast domain, producing an exceptionally narrow global maximum amid numerous secondary maxima. We show that higher-likelihood secondary maxima concentrate progressively around the global maximum and can therefore guide an adaptive contraction of the search volume. We exploit this structure through a reduced-dimensional profile likelihood and a coherent hierarchical strategy to search for EMRI signals across the full 14-dimensional parameter space. This enables the first end-to-end coherent parameter estimation for generic EMRIs with astrophysically broad priors. In stationary Gaussian LISA noise, the search recovers two half-year analytical-kludge signals with signal-to-noise ratios near 50, yielding fitting factors of 0.989 and 0.971, fractional errors of $10^{-3}$–$10^{-2}$ in the phase-evolution parameters and near $3\%$ in the distance, and error of less than $0.1$ radian in the sky location. The method turns secondary maxima into guides for a coherent hierarchical search.