General Relativity and Quantum Cosmology

We formulate the closure problem for first-order, traceful radiation-gauge metric reconstruction on a Kerr background with matter. The reconstruction is decomposed into Weyl-curvature, Ricci-trace, and mass--angular-momentum completion sectors. For compatible initial, gauge, and completion data, we establish local existence and uniqueness of the resulting triangular transport system on a regular Kerr domain, and identify the additional conditions needed for a closed global formulation. This is not a global existence theorem. We test the framework using two conserved matter sources. For a thin shell around a Schwarzschild black hole, Israel matching, regularity, asymptotic flatness, a barotropic equation of state, and fixed rest mass determine the static, axial, and leading rotational sectors. The ADM-mass shift is $\sqrt{1-2M/R}$ times the shell rest mass, while the axial sector determines the angular momentum, moment of inertia, and interior frame dragging. We also construct a stationary constant-angular-momentum fluid torus on Kerr and compute its Newman--Penrose Ricci projections, showing that nonspherical sources generally excite coupled Ricci sectors. The shell provides a closed benchmark, while the torus illustrates the additional structure required for general Kerr sources.

Could a star orbiting one mouth of a wormhole make the mass seen near the other rise and fall? We show that the periodic mass change proposed for searches around Sgr A* does not occur. The predicted signal comes from treating static solutions with different masses as successive states of the same orbiting system. In the Maxwell analogue, charge measured around a mouth changes only when current crosses the measuring surface. Similarly, in gravity, source motion cannot change the observed Schwarzschild mass at first order. Furthermore, the Bondi mass of a vacuum observer end cannot increase even beyond first order, though gravitational radiation can reduce it. The same observer-side dynamics can be reproduced with both mouths in one exterior at sufficiently large separation.

We calculate first-order corrections to the energy, radial period, and circumferential turning radii of equatorial periodic orbits around rapidly rotating black holes in dynamical Chern--Simons (dCS) gravity. Using an analytic fit to the metric correction, we match each orbit to a Kerr reference at fixed dimensionless spin, dimensionless specific angular momentum, and rational periodicity. The period correction combines a direct contribution at fixed energy with compensation from the energy adjustment that preserves periodicity. Their competition produces sign changes across orbital families and reference paths. In a two-parameter scan, negative period corrections are dominated by energy compensation for sampled prograde orbits and by the direct contribution for sampled retrograde orbits. We locate $C_T=0$ boundaries, where the coefficient of the first-order fractional period correction vanishes. Circumferential shifts can differ in sign from coordinate shifts. Numerical kludge waveforms at leading quadrupole order and their discrete spectra connect these corrections to phase accumulation and harmonic frequency shifts. At fixed dimensionless orbital parameters and physical mass of the small body, this phase contribution can be reproduced to first order by rescaling the Kerr mass. For the $C_T=0$ orbit examined here, this contribution is suppressed at equal black hole masses, while corrections to the waveform and spectral amplitudes remain nonzero.

We study whether nearby homogeneous cosmological histories approach or move away from the Genesis and contracting solutions. We also determine how an uncertainty in the scalar velocity at a later stage affects the inferred initial velocity. In the Genesis models, including the gravitational dynamics can substantially change this relation. We find that convergence of homogeneous solutions can occur even around backgrounds with unstable perturbations, and therefore attraction of the background is not sufficient to establish that a cosmological solution is physically viable. In the contracting model, one power-law solution attracts nearby trajectories, whereas another repels them. The strength of these effects depends on how the cosmological state is parametrized. Their evolution through the subsequent bounce is not considered here.

We introduce a semi-agnostic modeling framework for black hole binary inspirals beyond general relativity that fixes the field content without selecting a particular theory. We expand in the post-Newtonian order and in powers of $l/L$, where $l$ is the characteristic length-scale that controls deviations from General Relativity and $L$ is the characteristic length-scale of the system. We focus on the case of a massless scalar field coupled with the metric, at leading post-Newtonian order. Taking into account the scaling with $l/L$ of both the interaction terms and the quantities that characterise the sources, we find that the inspiral can be described in terms of a small number of universal parameters. Such a parametrisation is suitable for obtaining combined bounds from multiple sources and performing searches for specific fields.

Shift symmetric Horndeski gravity can be a simple, well posed theory with protection against quantum corrections. Overturning conventional thought that such a theory cannot cross the phantom divide ($w=-1$) we present both analytic and numerical proof that it can. We carry out a detailed dynamical systems analysis showing the evolution of ghost free and stable regions within the model family, identify the fixed point and dynamical attractor structure, and derive the interaction of the $w=-1$ curve with these phase space structures. This reveals two mechanisms for cosmologies crossing the phantom divide while preserving shift symmetry.

We construct static black holes in Einstein-Maxwell-scalar theory under prescribed external scalar fields, mapping their existence domain and determining how their scalar charges vary with the external field. Focusing on solutions with positive scalar charge, we find that a positive external field induces scalar charge in Reissner-Nordström (RN) black holes below the zero-source scalarization threshold and extends the allowed charge-to-mass range. A negative external field instead introduces a finite lower existence boundary and permits distinct black holes under identical external conditions. Coupling these isolated responses through the leading companion-generated scalar fields, we find mutual scalar induction in binaries whose components are RN black holes in isolation. For binaries with scalar charges of the same sign, their scalar charges need not increase as the separation decreases, while some binaries with opposite scalar charges admit multiple equilibria and cannot continue along their original equilibrium branches to smaller separations.

Standard sirens provide a direct probe of the cosmic distance-redshift relation and therefore a powerful test of whether gravitational waves (GWs) propagate as predicted by general relativity on cosmological scales. In many extensions of general relativity, GW propagation is modified by an anomalous friction term, which alters the amplitude evolution and leads to a GW luminosity distance that differs from its electromagnetic counterpart. In this work, we develop a non-parametric reconstruction of this anomalous friction from dark standard sirens. We reconstruct its redshift dependence, encoded in the friction function $\alpha_M(z)$, with a Gaussian process (GP) and derive the corresponding GW-to-EM luminosity-distance ratio $\Xi(z)$ by integration, explicitly retaining the relation between the local friction modification and its accumulated effect on the observed distance, while enforcing a monotonic and invertible GW luminosity distance. We apply the method to the GWTC-5.0 catalog, jointly inferring the source population, modified propagation, and background cosmological parameters. We find no evidence for departures from GR, with $\alpha_M=0$ and $\Xi=1$ consistent with the posterior over the redshift range probed by the catalog. The result is stable under variations of the GP kernel, smoothness and amplitude priors, resolution prescription, and likelihood treatment. We further introduce function-space diagnostics for comparing flexible and parametric reconstructions, including prior calibration, prior-to-posterior contraction, common summaries of propagation-population degeneracies, and principal-component analysis. These tools make explicit which features are informed by the data and which are imposed by the function-space prior, providing a framework for interpretable non-parametric tests of gravitational-wave propagation.

This study develops a new gauge condition for performing long duration numerical evolutions of Einstein's equation on cosmological spacetimes with non-trivial spatial topologies. This new gauge makes it possible to perform reliable numerical evolutions on these manifolds in which the spatial volumes become more than one million times larger. This new condition was tested for this study by evolving homogeneous and isotropic initial data on exemplar manifolds with three spatial topologies: Sixth-Turn space, the lens space L(5,2), and the Seifert fiber space SFS[S2:(2,1)(2,1)(2,-1)].

We identify a unified dynamical picture connecting small-amplitude scalar input at the event horizon to scalar--Kasner interiors. Within boundary-supported stationary families, area contraction drives the transition from geometric to scalar kinetic dominance. For the Schwarzschild-like branch, contraction suppresses the relative curvature contribution, so the scalar kinetic term becomes dominant while the gradient remains small. For the Kerr--Newman-like branch, the scalar gradient is strongly amplified as area contraction carries the solution toward the would-be Cauchy-horizon zero, followed by a narrow transition to scalar kinetic dominance. Cancellation between the kinetic and geometric terms produces a positive minimum of a metric diagnostic, explaining inner-horizon loss dynamically. Fully coupled numerical solutions for the Schwarzschild-like branch and four-dimensional stationary axisymmetric Kerr--Newman interiors, including the Reissner--Nordström and Kerr limits, support this picture. Area contraction provides the common physical mechanism, while the would-be Cauchy-horizon zero determines the strength of gradient amplification and the localization of the transition.

In this study, we investigate the gravitational particle production (GPP) as a natural reheating channel in time-dependent backgrounds. We focus on reheating in an inflation-kination background. To maintain generality across inflationary models, we use a continuous scale-factor function that produces this transition and has been proposed in the literature. In this scenario, the gravitational reheating channel arises from the gravitational excitation of a superheavy spectator scalar field with Ricci-matter gravitational coupling. Besides all the perturbative approaches, a recently proposed non-perturbative one that uses the notion of the adiabatic vacuum has also been applied to the case of superheavy particles. Although the effect of the mass of the field on the reheating temperature has been investigated, the impact of the non-conformal values of the gravitational coupling constant on the GPP rate is not considered. Hence, we modify the non-perturbative approach in such a way that both effects can be traced. Three parameters affect the reheating temperature in this case: the bare mass of the field, the gravitational coupling constant, and the transition time. In this paper, the effect of each of these parameters alone on the resultant reheating temperature, as well as the combined effects of these parameters, is studied. Taking into account all involved parameters and surveying a wide range of the 3D parameter space, the highest reheating temperature possible is obtained. All of the aforementioned investigations are done based on numerical calculations, and we obtain that the highest possible reheating temperature is quite sufficient for the universe to enter the Hot Big-Bang era. For the sake of completeness, we study the GPP in such a transition using an analytical method in an independent, parallel, solvable model. This analysis is presented only as a mathematical tool.

This Letter investigates gravitational-wave tests of the horizon area law. Although they provide a striking consistency check of general relativity (GR), these tests rely on models that assume GR, making their interpretation inherently model dependent. We show with a specific example---simulations of merging boson stars---that exotic compact objects can mimic merging black holes and pass an area-law test at a confidence as high as $\sim 92\%$ despite not even having event horizons.

We present the first study of coexisting Vainshtein and Chameleon screening in cosmic structures. Screening hides fifth forces locally, keeping modified gravity viable. Realistic dark-energy models can activate several mechanisms at once, yet this interplay has been overlooked. We find that (i) the Chameleon resolves the long-standing Galileon void pathology; (ii) it suppresses or eliminates the Vainshtein radius around massive sources; and (iii) the Vainshtein term shrinks the Chameleon's screened core. These effects reshape the observable signatures central to cosmological tests of gravity.

We study the shadows of a charged rotating de Sitter solution in fourth order conformal Weyl gravity (CWG) immersed in plasma and analyze the joint charge-plasma constraints. Our main goal is to distinguish observational effects caused by the dispersive plasma environment from those caused by the underlying gravitational theory. Within a separable Hamilton-Jacobi plasma model, we derive the radial and angular photon potentials, the equatorial finite-distance deflection angle, and the finite-observer shadow boundary due to the asymptotically non-flat nature of the CWG spacetime. Our results separate two effects. Increasing the plasma strength generally reduces the shadow radius, the signed deflection angle, and the energy emission peak in both CWG and GR. Charge ($q$) produces a stronger theory dependence: for the representative parameters studied, increasing $q$ enlarges the CWG shadow but reduces the GR shadow. The lensing behavior independently supports the geometry-dependent response found from the photon region and shadow observables. We further compare the finite observer dimensionless shadow radius with EHT-inferred size intervals for Sgr~A$^*$ and M87$^*$. Our results indicate that plasma effects can mimic part of the shadow size shift, but the distinct charge response of CWG offers a potential observational route for separating conformal gravity signatures from environmental propagation effects.

A causal set is a locally finite partially ordered set. Causal set theory proposes such discrete structures as a basis for spacetime physics. Connecting this description with continuum physics requires recovering the geometric quantities used in general relativity and controlling the errors introduced by discreteness. Here, with dimension and sampling density specified, we construct approximate normal coordinates, estimate parallel transport, and recover the full Riemann tensor from causal order and element counts. For samples embedded in a fixed smooth spacetime and satisfying stated uniform counting assumptions, we prove a uniform curvature error bound that tends to zero as the sampling density increases.

Gravitational-wave (GW) observations of binary black holes provide a powerful probe of general relativity (GR) in the strong-field regime. In effective field theory (EFT) extensions of GR, higher-curvature operators modify the binary dynamics and introduce corrections to the inspiral phase. In this work, we consider two parity-even cubic-curvature couplings and one quartic-curvature coupling, whose leading phase corrections enter at 5PN, 6PN, and 8PN order, respectively. We incorporate these corrections into the individual multipoles of the \texttt{SEOBNRv5HM\_ROM} waveform using the flexible theory-independent framework, allowing higher-order modes and the full inspiral-merger-ringdown signal to be used in the analysis. We first perform a Fisher-matrix analysis of 92 binary-black-hole events selected from a parent sample of 273 events in the public LIGO-Virgo-KAGRA catalogs. GW230627\_015337 provides the tightest forecast constraints on all three EFT couplings and is therefore selected for a full Bayesian analysis. The posterior distributions are consistent with GR, with all three couplings consistent with zero at 90\% credibility. The corresponding one-sided 90\% upper limits on the characteristic length scales are $17.1$, $11.1$, and $18.3\,\mathrm{km}$. The log Bayes factors of the three EFT models relative to GR range from $-5.49$ to $-2.51$, favoring GR under the adopted priors. These bounds probe higher-curvature length scales at the level of $10$--$20\,\mathrm{km}$ and are numerically tighter than representative previous inspiral and ringdown constraints, although differences in the models and analysis assumptions should be taken into account.

This paper investigates the greybody factor and Joule-Thomson expansion of deformed Schwarzschild-AdS black hole models. We constructed the Klein-Gordon equation into a Schrödinger-like wave equation using tortoise coordinates and derived the exact effective potential. Also, we analyzed its behavior under varying physical parameters, including deformation parameters, mass and angular momentum. In this case, our results illustrate that increasing the deformation parameter enhances the effective potential, significantly impacting the absorption and scattering of massless scalar fields. It is noted that the Schwarzschild black hole effective potential is greatly increased when the deformation parameter is present. Near the event horizon, we found that waves behave differently, with higher-frequency waves more easily penetrating potential obstacles and lower-frequency waves bouncing off them. Furthermore, we investigated the thermodynamic characteristics of black holes using the Joule-Thomson expansion, detecting isenthalpic curves that indicate heating and cooling zones controlled by pressure and temperature changes. In this context, we tested the influence of deformation black hole parameters; the isenthalpic curves are enhanced by increasing the deformation parameters and the black hole mass.

By treating black-hole states as topological defects in thermodynamic parameter space, we investigate a static, asymptotically flat magnetic black holes in Einstein gravity coupled to causal nonlinear electrodynamics. Using the generalized off-shell free energy and Duan's $\phi$-mapping topological current theory, we analyze the physical single-horizon sector in the canonical ensemble. We identify four representative defect-curve profiles, including realizations of the conjectured $W^{0+\leftrightarrow1-}$ class and $\overline{W}^{1-}$ subclass, as well as a new thermodynamic topological subclass, $\overline{W}^{0+\leftrightarrow1-}$. This new subclass features paired generation and annihilation points, with unstable innermost and outermost branches. As the auxiliary inverse temperature increases, the system evolves from two equilibrium states to three and then back to one, with an unstable small-black-hole defect entering through the physical lower boundary and changing the global topological number from $W=0$ to $W=-1$. This boundary-induced change signals a thermodynamic topological phase transition. These results show that the same inverse-temperature endpoint behavior and winding-number sequence from small to large black holes can accompany different defect evolution, highlighting the role of the physical horizon boundary in thermodynamic topological classification. More broadly, this causal nonlinear-electrodynamics black-hole family provides a setting for discovering further defect structures and thermodynamic topological phase transitions.

We investigate the hydrostatic equilibrium and global structure of neutron stars within symmetric teleparallel gravity, where gravitational interactions are mediated by the non-metricity scalar $Q$. Working within the metric-affine formulation, we adopt the regular, constant-$Q$ branch ($Q = Q_*$) of $f(Q)$ gravity, which preserves regularity at the stellar centre while maintaining explicit dependence on the non-linear functional form through $f(Q_*)$ and its derivatives. We propose three novel non-linear $f(Q)$ extensions: (i) a Born-Infeld-inspired model, (ii) a Hu--Sawicki analogue, and (iii) a Tsujikawa-inspired model. Incorporating state-of-the-art realistic unified equations of state, namely GPPVA(DD2) and SLy4, we numerically solve the modified Tolman-Oppenheimer-Volkoff equations and evaluate stellar stability via the Harrison-Zel'dovich-Novikov criterion. The Born-Infeld and Hu-Sawicki analogues smoothly recover the general relativistic limit as their control parameters increase, predicting stellar radii for low-mass objects ($M < 2.0\,M_\odot$) that match observational constraints from X-ray binaries and GW170817; however, their maximum masses remain capped below $2.43\,M_\odot$ (DD2) and $2.06\,M_\odot$ (SLy4). Conversely, the Tsujikawa-inspired model significantly stiffens the effective gravitational coupling, accommodating massive compact objects up to $\sim 3.36\,M_\odot$ and offering a viable physical origin for the $2.59_{-0.09}^{+0.08}\,M_\odot$ secondary object in GW190814, albeit at the expense of overpredicting radii for typical low-mass neutron stars. These contrasting behaviours demonstrate a key phenomenological complementarity between maximum mass and radius bounds within the constant-$Q$ framework, highlighting the utility of multimessenger observations in constraining non-linear non-metricity gravity.

We study the possibility of the formation of primordial black holes (PBHs) using an inflaton potential constructed by stabilizing all Kähler moduli employing both the perturbative and non-perturbative corrections in the large volume scenario in type-IIB/F string theory. We further introduce a small perturbation in one of the Kähler moduli that modifies the existing potential in the field space. The effective correction in the moduli space is made by introducing a localised Gaussian bump, which induces an ultra-slow-roll feature in the inflaton potential during the early cosmological inflation. The evolution of the amplitude of the curvature power spectrum is solved numerically by using the Mukhanov-Sasaki equation, with Bunch-Davies initial conditions. The inclusion of the Gaussian bump produces a sustainable enhancement in the amplitude of curvature power spectra around $k\sim 1.12 \times 10^{9} Mpc^{-1}$ for the formation of PBHs. The abundance of PBHs ($f_{PBH}$) is calculated using the Press-Schechter formalism for different values of critical density contrast and presented in the background of contemporary $f_{PBH}$ bounds and checked for viability with existing microlensing bounds, corresponding to a mass value $10^{-6}M_\odot$ for $\delta$ threshold value $\delta_c=0.439$. The Hawking temperature and evaporation time are also determined for these black holes and found to be of the order of $2.78\times 10^{-15}$ GeV and $8.5\times10^{38}$ Gyr, respectively. The enhancement of curvature power spectra lies in the sensitivity region of the SKA observations, suggesting an indication that scalar-induced gravity waves may be probed in future observations.

We formulate a description of self-gravitating Schrödinger--Poisson (SP) solitons in curved spacetime using a local inertial frame centered on the soliton. In the weak-field and non-relativistic regime, the effect of the background spacetime is incorporated into the SP equations through an effective tidal potential determined by the spacetime curvature. We apply this framework to a soliton moving along a circular equatorial geodesic around a Kerr black hole. The tidal field contains stationary and time-dependent quadrupolar components, which induce a deformation of the soliton and an associated mass quadrupole moment. We formulate the quadrupolar response in terms of the tidal deformability and the dimensionless Love number. We then estimate the gravitational radiation associated with the rotating deformed soliton and evaluate the corresponding characteristic strain for representative soliton sizes and orbital radii. A comparison with representative sensitivity curves of planned space-based gravitational-wave detectors identifies parameter regimes in which the estimated characteristic strain may lie within their sensitivity ranges. Our framework provides a systematic basis for investigating the tidal response of self-gravitating bosonic solitons in black-hole spacetimes and their potential gravitational-wave signatures.

One of the central expectations of quantum gravity is the resolution of the curvature singularities predicted by General Relativity, potentially giving rise to effective black-hole geometries that are regular inside the horizon. We show that, for a very broad class of regular black holes including several known solutions, the quasinormal-mode spectrum in the large-overtone limit differs discontinuously from that of a Schwarzschild black hole, even when the regularization parameter is arbitrarily small. The real part of the quasinormal frequencies vanishes asymptotically, rather than approaching a nonzero constant, as generically occurs in General Relativity and other theories predicting black holes with curvature singularities. The asymptotic black-hole spectrum thus retains a distinctive imprint of singularity resolution. We establish these results analytically through a systematic formulation of the monodromy method and confirm them numerically. We interpret this phenomenon as a manifestation of black-hole spectral instability, whereby arbitrarily small deviations from vacuum General Relativity produce nonperturbative changes in the large-overtone spectrum.

We construct a Genesis scenario within the framework of a type-II minimally modified gravity. The background solution is past geodesically complete and approaches Minkowski spacetime in the asymptotic past. While the Hubble expansion rate grows, the matter sector satisfies the null-energy condition. Scalar perturbations are ghost-free and have no ultraviolet gradient instability, although the squared sound speed $c_\mathcal{R}^2$ becomes negative within a finite infrared region in the Fourier space for a finite time interval. Numerical evolution, including superhorizon growth, yields a nearly scale-invariant, slightly red-tilted scalar spectrum over a broad region of parameter space. The tensor spectrum is blue, with a strongly suppressed tensor-to-scalar ratio. Finally, using the matter fluctuation $\delta\chi$, whose asymptotic normalization is regular, we find that the background-dependent cubic couplings vanish in the far past at fixed nonzero momenta. The surviving matter--graviton and graviton self-interactions are Planck suppressed.

We use the modified Newman--Janis algorithm to obtain the rotating ``mother'' black hole solution of the rotating Hayward-AdS black hole. We further derive the fundamental thermodynamic quantities of the ``mother'' black hole in the full unconstrained phase space $(S,J,q,\alpha,P)$, and impose the regularity condition $M_1=q^3/\alpha$ to obtain the thermodynamic quantities of the rotating Hayward-AdS regular black hole. This order of operations gives a Hawking temperature identical to the surface gravity temperature and produces the correct response functions of the regular black hole. For $P<P_c$, the Hawking temperature $T_2$ possesses a local maximum and a local minimum, which divides the black hole into small, intermediate, and large black hole branches, and the $P$--$V$ isotherms display oscillatory behavior characteristic of a liquid/gas phase transition. The small and large black hole branches are locally stable, whereas the intermediate black hole branch has negative heat capacity and is locally unstable. Increasing the rotation parameter $a$, magnetic charge $q$, or pressure $P$ reduces the region of the intermediate branch. The $G_2$--$T_2$ diagram shows that the phase structure, in contrast to the standard swallowtail of the Reissner--Nordström-AdS and Kerr--Newman-AdS black holes, is 8-shaped or C-shaped. These two shapes are divided by the characteristic pressure $P_z$. For $P<P_z$, the curve is 8-shaped, corresponding to a first-order small/large black hole transition. For $P_z<P<P_c$, the curve is C-shaped, corresponding to a zeroth-order transition. These results show that the 8-shaped/C-shaped phase structure characteristic of regular AdS black holes persists under rotation, indicating that it stems from the restructuring of the thermodynamic phase space by the regularity condition rather than from spherical symmetry.

We study a canonical scalar field coupled to isotropic triplets of Abelian one-forms and two-forms through scalar-dependent kinetic functions and a constant topological $BF$ interaction. By retaining the lapse in the homogeneous reduction, we recover the Friedmann constraint and identify a sufficient domain in which all twelve physical modes have positive kinetic terms and luminal high-frequency propagation. A separate exponential model admits an accelerating mixed solution with $a\propto t^2$, nonzero asymptotic form fractions, and bounded normalized linear perturbations. For the Noether analysis, we choose a quadratic effective potential in flat minisuperspace coordinates and solve the zero-boundary determining equations. The canonical scalar potential is hyperbolic-squared or exponential, rather than a power law in the scalar field. The causal character of the potential coordinate separates three branches: Branch I admits a de Sitter limit, Branch II cannot sustain acceleration on regular future-complete expanding trajectories, and Branch III gives an exact solution with both form sectors active and late expansion $a\propto t^{4/3}$. Comparisons with consistent uncoupled and reduced-field limits separate the form contributions from the scalar-driven acceleration. The $BF$ term changes the finite-time exchange between the form sectors but supplies no direct negative-pressure source.

In this work, we investigate the geodesic dynamics and tidal force effects in neutral and electrically charged regular spacetimes inspired by T-duality. We first analyze the geometric properties of these solutions, including their regular central structure and horizon configurations, and show how the interplay between the T-duality scale $\ell_0$ and the electric charge $Q$ determines the transition between black hole and horizonless geometries. We then study the motion of massive and massless particles through the corresponding effective potentials, examining the existence and stability of circular orbits and the behavior of their characteristic radii. We further investigate the tidal forces experienced by observers in radial free fall, focusing on the behavior of the radial and angular components, their extrema and sign changes, and the location of these characteristic points relative to the horizon structure of the geometry. We show that the T-duality regularization renders the tidal forces finite in the central region and gives rise to different stretching and compression regimes, including a region of simultaneous compression in both the radial and angular directions, while the electric charge modifies the strength and location of these tidal features. Finally, we analyze the evolution of the geodesic deviation vector for two sets of initial conditions. We find that both the T-duality scale and the electric charge tend to suppress the accumulated radial stretching, whereas the angular deformation is considerably less sensitive to the charge. These results show how the quantum regularization induced by T-duality and the presence of electric charge modify the orbital dynamics and tidal response of these geometries in the strong-field regime. Furthermore, we demonstrate that the corresponding classical limits are recovered appropriately.

We study scalar and electromagnetic perturbations of a Schwarzschild black hole (BH) surrounded by a dark matter halo described by the King density profile. The lapse function can be expressed as $1-2[M+M_{\rm DM}(r)]/r$, where $M_{\rm DM}(r)$ is the halo mass enclosed within radius $r$; thus, the halo affects the geometry through its enclosed-mass function. We compute the quasinormal frequencies using the sixth-order WKB method and its Padé-improved version. Rewriting the lapse function in terms of the inverse hyperbolic sine avoids the severe numerical cancellations that arise when evaluating its high-order derivatives. For the configurations examined, the fundamental frequencies agree with those extracted from time-domain evolution to within $0.2\%$.The halo lowers both the oscillation frequency and the damping rate. The change of the real part is almost entirely accounted for by the halo mass enclosed by the photon sphere, and the additional decrease of the damping rate follows the ratio of the Lyapunov exponent to the angular frequency of the circular null orbit. Since part of the halo lies inside the horizon in this metric, we also place the halo outside the BH by means of an Einstein cluster. The frequencies then decrease by a similar amount, but the real part follows the Schwarzschild value multiplied by the gravitational redshift factor of the halo. A jump in the density at the inner edge of the halo scatters the waves and changes the damping rate by up to about $9\%$. For a continuous density profile, deviations from the redshift relation remain below about $1.5\%$ for $r_{\rm in}=3M$ and below about $0.5\%$ for the cases with $r_{\rm in}\geq4M$. No unstable modes are found within the perturbation sectors and parameter configurations examined.

Rotating black holes offer powerful probes of gravity, but constructing their geometries beyond vacuum general relativity remains challenging. Here we develop a unified framework for constructing stationary, axisymmetric deformations of Kerr from their tidal curvature and physical sources. As a demonstration, we obtain closed-form solutions for six higher-curvature interactions at leading order in the couplings and for generic subextremal spin, without slow-rotation expansions, numerical fitting, or mode decomposition. The solutions pass stringent checks against the field equations, previous mode-by-mode constructions, and known analytic predictions for horizon quantities. We find that the chirality of the interactions organizes the analytic structure of these solutions, a pattern that likely extends to a large class of purely metric higher-curvature theories. Our framework opens a systematic route to black-hole geometries in beyond-Einstein theories and perturbative astrophysical environments. These geometries provide a foundation for strong-field tests with gravitational waves and other observational channels, such as black-hole images and X-ray spectroscopy, as well as theoretical studies of near-extremal black holes.

We investigate how deviations from the Schwarzschild geometry affect the motion of massive test particles and the gravitational radiation associated with their periodic trajectories around a new improved Schwarzschild black hole. Periodic configurations are determined by examining the commensurability of the radial and azimuthal orbital frequencies. For representative trajectories, we numerically reconstruct the particle motion and calculate corresponding gravitational wave polarizations using the symmetric trace-free mass-quadrupole approach. By comparing these signals with their Schwarzschild counterparts, we assess how the modified spacetime geometry is encoded in the radiation. Our analysis shows that the parameters $\xi$ and $\gamma$ produce modest changes in the orbital configurations and their associated waveforms, providing a means of investigating the dynamical signatures of this BH model.

It is commonly assumed that the mass of dark matter particles cannot be determined from their gravitational effects when dark matter behaves as collisionless matter. Here we show that extreme-mass-ratio inspirals observable by millihertz gravitational-wave observatories such as the Laser Interferometer Space Antenna (LISA) could measure the mass of ultralight dark matter particles in sufficiently dense dark matter spikes. The separation of scales between the two black holes allows ultralight dark matter to form a collisionless density spike around the massive primary while retaining wave effects in its interaction with the stellar-mass companion. We incorporate wave-dependent accretion and dynamical friction into relativistic inspiral waveforms and jointly infer the dark matter particle mass, spike normalisation and binary parameters from simulated LISA signals. For massive black holes at the low-mass end of the LISA population ($M\sim 10^5 M_\odot$), our forecasts show that particle masses spanning $10^{-14}-10^{-11}\,\mathrm{eV}$ could be measured to within an order of magnitude.

It has been proposed that consistency limits how slowly black holes can ring down in extensions of General Relativity: effective-field-theory (EFT) corrections may lengthen the decay time of a quasinormal mode by at most about one oscillation period, $\Re[\omega_{\rm GR}]\,\delta\tau\lesssim1$. We argue that, under standard power counting, this condition yields no new, model-independent constraint on gravitational EFTs. First, its motivation does not extend straightforwardly to black holes: the inverse oscillation frequency is not a universal, detector-independent uncertainty in the damping time of a classical waveform. Our main argument, however, rests on eikonal power counting alone. The decay-time shift grows with the angular momentum $\ell$ of the mode, but so does the weight of higher-derivative operators. When curvature and derivatives are controlled by a single scale $\Lambda$, as in every known ultraviolet completion, the EFT around a black hole of radius $r_s$ remains predictive up to $\ell\sim(r_s\Lambda)^2$, and the shift becomes of order one only there, where an infinite tower of operators contributes at the same order. A resolvable shift within the predictive regime requires either large numerical coefficients or a two-scale power counting, which has no known ultraviolet completion. In both cases the quartic-curvature operators dominate, and the condition coincides parametrically with the positivity bounds that flat-space graviton amplitudes impose under standard assumptions on the ultraviolet completion. Only in scalar--tensor theories could the two-scale window probe beyond positivity, and then at most one family of dimension-ten operators. The axial sector of Einstein--dilaton--Gauss--Bonnet gravity and Einstein--Maxwell theory illustrate these results.

String compactifications and runaway-dilaton models can contain light scalar directions. Motion along these directions changes gauge couplings, the QCD scale, quark masses, and Yukawa parameters. A given string-derived sector then predicts low-energy slopes. Its gauge kinetic functions, matter-metric or Yukawa slopes, source charge, scalar trajectory, and scalar range determine a Damour--Donoghue weak-equivalence-principle (WEP) vector and a clock-drift vector. The fit assumes one long-range scalar or an aligned multi-field direction. With that assumption, WEP tests and secular clock drifts probe related projections of the same scalar-slope vector. The minimal two-charge Damour--Donoghue fit uses Ti--Pt MICROSCOPE, Be--Ti torsion-balance, and $^{85}$Rb--$^{87}$Rb atom-interferometer data, then adds the Yb$^+$ E3/E2 secular $\alpha$-drift row. The WEP-only fit gives $D_{\hat m}=(-6.06\pm34.91)\times10^{-12}$ and $D_e=(8.80\pm46.46)\times10^{-12}$, with correlation $-0.99958$. The clock input is $\dot\alpha/\alpha=1.0(1.1)\times10^{-18}\,{\rm yr}^{-1}$. It matches the WEP marginal reach when $|\zeta|=2.37\times10^{-8}\,{\rm yr}^{-1}$, with $\zeta=\dot\varphi/\alpha_E$. For the benchmark $\dot\varphi=\xi H_0$ and $\alpha_E=10^{-3}\alpha_0$, this gives $\xi/\alpha_0\simeq0.34$. A model becomes testable after it supplies $r=D_{\hat m}/D_e$, the scalar amplitude, and $\zeta$. The Damour--Piazza--Veneziano runaway-dilaton estimate lies near $\eta\sim10^{-12}$ for order-unity $n=2$ parameters, well above the MICROSCOPE-level WEP scale. In the representative-isotope two-charge model, a MICROSCOPE-level Be--Ti-like row would reduce the long WEP axis by a factor $27.8$; a repeated Ti--Pt-like row would barely change it. The calculation tests compactification-level predictions for string-derived dilaton or modulus sectors after the model supplies its low-energy data.

We demonstrate the formation and subsequent evolution of Julia--Zee dyons in $(3+1)$-dimensional classical lattice simulations of an $\mathrm{SU}(2)\to\mathrm{U}(1)$ symmetry-breaking model in an expanding background. The gauge and Higgs fields are prepared thermally, subjected to an ultraviolet filter, and evolved through a mass quench and subsequent expansion. Classical dyons can carry continuous electric charge, and we find charge magnitudes exceeding four times the electric charge unit $g$. Their measured electric-charge magnitudes tend to decrease during the subsequent evolution, consistent with charge exchange with the surrounding fields. At late times, the magnetic monopoles persist while the number of dyons and their observed charge range decrease, with only a few identified dyons remaining at the end of the simulations.

The family of $SL(2,\mathbb Z)$ black holes has an accumulation point corresponding to a cusped geometry, which causes the sum over black holes to diverge. We extend cusp regularization to the sum over geometries compatible with a fixed boundary spin structure. For $c_L=c_R$, including the cusp as a counterterm cancels the leading divergence for each of the three even boundary spin structures. The required subtraction is the same in all three sectors and is two thirds of the bosonic one. We further show that gravitational anomalies cause cancellations between black hole contributions, removing the leading cusp divergence except at $c_L-c_R=0,\pm24$ in pure gravity and $c_L-c_R=0,\pm12$ in $\mathcal N=(1,1)$ supergravity. We also derive the spin structure dependent anomaly phases responsible for these cancellations.

The relic abundance of light stable axion dark matter is usually set by misalignment. We study whether the inflationary fluctuations of the axion can dominate instead, and we follow the modes analytically through an instantaneous transition from de Sitter expansion to radiation domination, neglecting the axion mass during inflation and keeping it afterward. Since the energy density is quadratic in the field, a fluctuation-dominated abundance carries an isocurvature perturbation even when the mean displacement vanishes. For a canonical minimally coupled axion the spectrum is scale invariant, and fluctuation-dominated dark matter exceeds the Planck isocurvature limit by about eight orders of magnitude. An inflaton-dependent kinetic function or a nonminimal coupling to the Ricci scalar tilts the spectrum blue, moving the fluctuation power from CMB scales to small scales. Imposing the Planck limit at the pivot scale, we find that fluctuation-dominated dark matter with a constant kinetic slope requires the spectral tilt $n_\eta-1\gtrsim0.27$ and the axion mass $m_{\eta} \gtrsim200 \rm{GeV}$ at $H_I=10^{10}\rm{GeV}$, and $n_\eta-1\gtrsim0.34$ and $m_\eta\gtrsim4.5\,$keV at $H_I=10^{13}\rm{GeV}$. A kinetic function with a running slope lowers these masses to $1.4~\rm{GeV}$ and $0.7\,$eV, respectively. For the QCD axion, whose oscillations start late, we estimate that any single power-law spectrum blue enough to satisfy the pivot limit gives too little fluctuation abundance, and misalignment dominates.

We investigate axionic quintessence in heterotic string compactifications. Starting from the ten-dimensional theory, we derive the four-dimensional axion effective action, including gauge couplings and non-perturbative potentials, and identify the curvature terms that can correct it. We examine the geometric requirements for ultralight axions generated by exponentially suppressed worldsheet instantons, finding significant restrictions through an exploratory scan of toric Calabi-Yau hypersurfaces. In an illustrative K3-fibred setup, the minimal benchmark also encounters a tension with the positivity of the one-loop corrected gauge kinetic functions. Aligned worldsheet-instanton contributions provide a way to alleviate this tension and yield an ultralight axion with a phenomenologically relevant decay constant. Our analysis also identifies lower-action instantons whose contributions must be controlled to preserve the ultralight axion. We then study the resulting class of quintessence potentials and qualitatively compare their late-time cosmological solutions with observationally preferred ranges.

The gravitational-wave spectrum produced by ultra-relativistic bubbles in a first-order cosmological phase transition can be approximated in terms of their energy density as a function of bubble size. Bubble collisions and post-collision classical evolution negligibly change it. The dominant energy loss is particle scattering, often in the Landau--Pomeranchuk--Migdal regime. So the GW spectrum depends on the particle-physics coupling (interpolating between the `envelope' and `bulk flow' limits), on the interaction type (gauge, Yukawa, scalar quartic, ...), and on whether particle number is conserved. Finally, we consider broken global symmetries, which give a mixture of `elastic' and `inelastic' collisions.

We propose a novel test for the hypothesis that the dark matter of the Universe is composed entirely by asteroidal-mass primordial black holes. It relies on detecting the stochastic gravitational-wave background generated by the coalescence onto rapidly spinning supermassive astrophysical black holes of the light primordial black holes accumulated in spherically symmetric spikes. We discuss the scenarios in which the signal can be observed by the future space-based gravitational-wave observatories LISA and DECIGO.

We investigate inflationary magnetogenesis driven by a non conformal coupling in the case of large-field $\alpha$-attractor inspired models. We introduce potential-dependent electromagnetic coupling functions $f(\phi)$ that reproduce the scaling $f\propto a^p$ during slow roll. Starting from Starobinsky inflation, we analytically derive explicit couplings for $(E)$-model and $(T)$-model potentials. We then study how these functions affect electromagnetic amplification in the regime of non-minimal coupling between the inflaton field and the Ricci scalar $\phi^2 R$. In particular, we compare different values for the coupling strength $\xi$, accounting for electromagnetic backreaction and Schwinger pair production through the gradient expansion formalism. Our numerical results show that the non-minimal coupling affects the evolution of the electromagnetic sector and the resulting magnetic-field amplitude. We find that, within the analyzed configurations, minimally coupled and $\xi>0$ scenarios are compatible with the adopted CMB constraints, yielding conditional present-day magnetic-field estimates of order $10^{-23}$ G.

These lectures provide an introduction to modern techniques for studying the analytic properties of loop-level scattering amplitudes and correlation functions in perturbative quantum field theory. We begin by developing the ideas behind Landau analysis, which identifies the location and nature of kinematic singularities in Feynman integrals (the universal building blocks that contribute to perturbative amplitudes and correlators). We then show how fundamental principles such as unitarity and causality constrain the analytic structure of Feynman integrals, and develop methods for working out some of these constraints in practice. Finally, we connect these observations to the properties of iterated integrals and their symbol calculus, to show how bootstrap methods can be used to determine the functional form of Feynman integrals from just knowledge of their analytic structure. These notes are based on a series of lectures held during the La Ricotta Summer School "The Disordered Universe 2025" from 21~July to 1~August~2025.

The dynamics of fermions in spacetime generates torsion, ultimately leading to a current-current interaction independent of gravity. This torsional four-fermion interaction is generically chiral and non-universal and may have observable consequences. Furthermore, the fermion basis in which this torsional interaction is diagonal may be different from the mass basis and the flavor basis. We work out the structure of the quark sector, where new CKM-like matrices appear as a result of diagonalizing the torsional interaction. CP violation is modified in general due to the appearance of additional phases. We also consider various processes which are affected by it such as kaon decays in particular and show that even when the torsional interaction is taken to be diagonal in the flavor basis, flavor-changing processes are still affected due to the non-universality of the torsional coupling constants. Finally, we discuss rephasing invariants in the presence of the torsional interaction and show how the Jarlskog invariant is modified even when the torsion basis is aligned with the flavor basis.

The complete Wess-Zumino (WZ) action and stress-energy tensor (SET) of the conformal anomaly in both two and four dimensions is given. This local effective action is expressed in terms of a single scalar Nambu-Goldstone `conformalon' field $\varphi$, parametrizing the local abelian Weyl group of conformal transformations that act transitively on the spacetime metric. Satisfying WZ consistency, and equipped with a variational principle for $\varphi$ that determines the conformal transformation $g_{\mu\nu}\!\to\!g_{\mu\nu}e^{-\varphi}$ to an associated spacetime with no anomaly, the WZ action resolves the conformal gauge fixing ambiguity of earlier methods of `integrating the anomaly.' In $D\!=\!2$ the WZ action is the local form of the Polyakov action, whose massless $\varphi$ propagator describes a correlated two-particle scalar intermediate state in the SET polarization function $\langle TT\rangle$. The imaginary part of this polarization obeys a UV finite sum rule, becoming a Dirac $\delta$-function at zero energy for conformal quantum fields, demonstrating the infrared origin of the anomaly, while the real part becomes the light cone propagator of $\varphi$. Although the $\Box R$ term in $D\!=\!4$ corresponds to a cohomologically trivial cocycle, it also arises from the IR limit of massless quantum fields, independently of UV physics, and contributes to the WZ action for low energy gravity. Analogous to the WZ action for pseudo-Goldstone mesons in low energy QCD from the axial anomaly, the WZ action for the conformal anomaly provides a Nambu-Goldstone scalar field for macroscopic gravity, in addition to the metric of classical general relativity.

Recent cosmological data provide weak hints for smaller masses than what is required by neutrino-oscillation experiments, motivating investigations into variation of the neutrino masses with cosmic time. Here we study a model where the neutrinos couple to a quintessence field that acts as dark energy. We compute structure formation using fully dynamical and relativistic N-body and lattice simulations, with nonlinear field evolution and a weak-field metric expansion. Similar to previous studies, we find the generic appearance of neutrino lumps, but observe them to be highly dynamical and spinning. We study several models where the effective dark energy, including nonlinear effects of the scalar field on the cosmic expansion, can show phantom crossing. The relativistic physics available in our simulation framework can help distinguish such models from LCDM, through observations of neutrino and dark energy properties, and slip between the gravitational potentials due to anisotropic stress. The rich phenomenology offered by mass-varying neutrinos motivates further exploration and development of the simulation techniques.

Effective field theories (EFTs) offer a powerful method to unify diverse models under a small set of control parameters, allowing systematic expansions around well-established theories. While these techniques were traditionally developed for particle physics experiments with clean, isolated initial states, realistic macroscopic environments are often noisy and dissipative. Recognising the limitations of traditional EFTs has recently sparked intense progress at the interface of high-energy physics and condensed matter. These developments motivate a new approach to gravitation and cosmology, one that models the gravitational sector as evolving in the presence of an unobservable medium. Open Effective Field Theories provide a systematic, controllable framework for this endeavour. This chapter presents this versatile framework and illustrates how the Schwinger-Keldysh formalism captures the influence of unknown environments, manifesting as dissipation and noise, on observational probes. These notes are based on a series of lectures held during the La Ricotta Summer School "The Disordered Universe 2025" from 21 July to 1 August 2025.

These lecture notes provide an introduction to quantum spin glasses, with a particular emphasis on their application to open problems in cosmology and holography. Focusing on the spherical $p$-spin model, we develop a complete and self-contained analysis of its thermodynamic and dynamical properties. We introduce the replica method, discuss both replica-symmetric and one-step replica symmetry-broken solutions, and characterise the resulting glassy phase. The framework is then extended to the quantum model, where we study the emergence of slow dynamics and the role of quantum correlations through Euclidean and real-time correlation functions. Finally, we explore how concepts such as replica symmetry breaking and disorder naturally arise in cosmological and holographic systems related to black hole fragmentation, highlighting spin glass models as useful theoretical laboratories for these phenomena. These notes are based on a series of lectures held during the La Ricotta Summer School: The Disordered Universe 2025 from 21 July to 1 August 2025.

We compute the normal mode spectrum and its spectral form factor for a probe scalar wave in smooth horizonless backgrounds. We first consider the BTZ black hole with a brickwall that hides the near-horizon region, which has recently been proposed as a toy model for a finite-temperature semiclassical black hole microstate. In this setup, the spectral form factor may or may not have a linear ramp, depending on the details of the brickwall construction. However, we argue that even in cases that do show a ramp, this ramp does not originate from level correlations associated with quantum chaos. Then we calculate the normal mode spectrum for a genuine microstate geometry (superstratum) and find evidence of chaos, both with a ramp and level repulsion. We conclude that the eigenvalue spectrum of normal modes can indeed serve as a tool for investigating the quantum dynamics of fuzzballs; however, the brickwall models are incapable of capturing this phenomenon.

A complete understanding of cosmology, from its earliest epoch all the way to the current dark energy dominated era, requires the development of a mathematical framework that incorporates quantum features in an expanding universe. Such a framework, alongside a description of the underlying degrees of freedom, is so far lacking. Several of the pertinent challenges and puzzles already arise upon considering even the most idealised model of an expanding universe --- the de Sitter spacetime and fluctuations thereof. In these lectures, we review some elementary ideas of the de Sitter physics, passing through the representation theory of the de Sitter group, aspects of canonical quantum gravity, all the way to attempts in describing quasi-local features. Throughout, we highlight open problems that motivate ongoing efforts to understand quantum gravity and cosmology in universes with $\Lambda>0$. These notes are based on a series of lectures held during the La Ricotta Summer School: The Disordered Universe 2025 from 21 July to 1 August 2025.

The Disordered Universe is a novel research direction that exploits ideas and techniques coming from apparently unrelated research areas, ranging from cosmology to scattering amplitudes in particle physics and disordered complex systems, with the aim of addressing open questions in cosmology at all scales, from the very infra-red (or very late time) to the early universe. This paper acts as a general introduction and vision for a set of lectures delivered at the first La Ricotta Summer School "The Disordered Universe 2025", held from 21 July to 10 August 2025. These lectures involved open quantum systems, analytic properties of scattering amplitudes and correlation functions, foundations and quantum aspects of the de Sitter universe, as well as statistical physics out of equilibrium and spin glasses. While the lecture notes related to each course taught at the school will be published separately and are inevitably devoted to both conceptual and technical aspects of each of these topics, the school was not meant to be a collage of independent topics: the present paper has the purpose of outlining the global vision, how cosmology ends up being a unifier and benefits from both their viewpoint and techniques, how all the concepts and techniques originally coming from these four different areas are part of the same cosmological narrative, why this point of view deserves to be explored, and drawing perspectives for the future. We consider it crucial to build a microscopic theory for the early universe and maybe one that embraces all scales.

KM3NeT has reported KM3-230213A, a $220$\,PeV neutrino with no source identified. If it comes from a cosmic-string network, energy conservation makes the event a calorimeter. The flux measures the power the network has spent, not how it emits, and a cusp at critical current can supply that power at unit efficiency. The event gives $G\mu\epsilon_p=(2.8\text{--}4.3)\times10^{-11}$ for $f_\nu=0.1$. Pulsar timing already reaches $10^{-10}$, so one event competes with the arrays. For the branch that still radiates gravitationally, flux and timing together require a third of the network's energy in particles, a share that further events above $100$\,PeV would measure.

Central extensions of asymptotic symmetry algebras are traditionally determined through an explicit computation of the algebra of conserved charges. We show that, within an ambiguity-free covariant phase space formalism based on the Noetherian split, they instead arise as intrinsic quantities completely determined by the Lagrangian through the geometry of the associated covariant phase space. We prove two general Charge Representation Theorems describing the canonical realization of diffeomorphism symmetries in the presence of field-dependent vector fields and Lagrangian anomalies, corresponding respectively to vanishing and integrable Noetherian flux. In both cases, we derive explicit expressions for the associated central extensions and establish the corresponding cocycle identities. This provides a constructive algorithm for determining central charges directly from the Lagrangian formulation of the theory, without requiring an explicit computation of the charge algebra. As a non-trivial application, we consider asymptotically locally AdS$_3$ spacetimes with Penrose--Brown--Henneaux boundary conditions. We recover the corresponding centrally extended asymptotic symmetry algebra, providing an explicit realization of the Charge Representation Theorems.

In light QCD axion models, finite-density corrections to the axion potential can source a nonvanishing axion field inside neutron stars. Extending our previous analysis of radial oscillations, we study the nonradial ($l=2$) oscillation spectrum of such axion condensed neutron stars in the relativistic Cowling approximation, keeping the fluid and axion perturbations fully coupled and dynamical. The condensate modifies the fluid spectrum in two ways: the altered equilibrium structure raises the $f$- and $p$-mode frequencies by up to $\sim20\%$, while the dynamical coupling to the axion field partially compensates this shift, almost entirely for the $f$-mode. Fluid modes with frequencies above the axion mass acquire a new damping channel through axion emission. The $f$-mode remains below this threshold for all configurations supporting a condensate, whereas the $p$-modes are damped on timescales that can be as short as $\sim10$ ms, shorter than their gravitational-wave damping times, except for certain axion masses where the outgoing axion amplitude nearly vanishes. The spectrum also contains a family of strongly damped axion-dominated quasinormal modes, with imaginary parts of order kHz, and a sequence of gravitationally bound axion states analogous to gravitational atom levels. Below the propagation threshold, the bound $p$-modes undergo avoided crossings with these levels, exchanging their fluid- and axion-dominated character.

We investigate single-field inflation models that can produce large curvature perturbations at sub-Mpc scales while remaining consistent with cosmological observations across multiple regimes. We highlight the tension between generating enhanced small-scale perturbations and maintaining agreement with the scalar spectral index $n_s$ measured by ACT and SPT, which disfavors several conventional single-field inflation models. To address this issue, we propose three viable classes of inflationary potentials: bump/dip-modified, step-like, and double-inflection-point. Each can sufficiently amplify primordial perturbations while predicting $n_s$ that lie within the $2\sigma$ range of current observational bounds. In addition, we examine the primordial power spectra predicted by these models and constrain their parameter spaces using cosmological observations at different scales, including CMB, BAO, PBH, PTA, and CMB-distortion. Our results show that some of the models considered can simultaneously satisfy the ACT/SPT constraints and account for the current PTA observations, although doing so while respecting the constraints on the PBH abundance remains challenging.

The nuclear equation of state shapes both the structure of rapidly rotating neutron stars and the orbital motion in their surrounding spacetime. Its uncertainty affects the mass and radius at which the innermost stable circular orbit reaches the stellar surface, a condition that defines the transition between disks whose inner edge is set by the surface and those truncated by orbital instability. We quantify how measurements of the electric dipole polarizability of neutron-rich nuclei reduce the uncertainty in this transition and in the orbital properties at the disk inner edge. We compute uniformly rotating neutron stars in general relativity for a family of equations of state that systematically vary the symmetry energy, derived from relativistic energy density functionals with density-dependent point-coupling interactions. We compare the results for the full family with those for the subset consistent with the measured dipole polarizabilities of finite nuclei. The dipole polarizability constraint reduces the spread in transition mass and equatorial radius by factors of about seven to ten across the spin frequencies considered. Along this transition, it also confines the orbital frequency at the disk inner edge to a band narrower than $20$~Hz at each spin. Combined with a measured neutron-star spin, a kilohertz quasi-periodic oscillation interpreted as disk orbital motion further restricts the mass--radius region, allowing an independent mass estimate to probe the symmetry-energy constraint. The dipole response of finite nuclei thus informs both the structure of rotating neutron stars and the orbital properties of their inner accretion disks.

Exact normalizable solutions of quantum constraints form a symplectic submanifold of the space of rays, whereas classical first-class constraints define a surface on which the symplectic form is degenerate. We ask how the degenerate directions can be recovered when quantum theory is regarded as fundamental and the constraints are imposed through a single positive master operator. For a nonnegative master function whose zero set is a Morse--Bott critical manifold, the image of the linearized Hamiltonian vector field is the symplectic orthogonal of the zero set, and coisotropy is equivalent to this linearization having square zero. The image is fixed by the zero set, but the theorem identifies it with the response of the master dynamics, which makes it accessible to quantum states. Three realizations follow. The exact quantum physical space is the opposite, rotational case of the same dichotomy. For quadratic masters, the bottom of the spectrum is $(\hbar/2)\Tr_+L$, so first-class zero sets carry no offset of order $\hbar$; within the harmonic approximation this explains the $\hbar$ versus $\hbar^2$ offsets observed in tests of the master-constraint programme. Finally, the second time derivative of the limiting covariance of a semiclassical packet, which can be determined by bounded probes, has the gauge distribution as its image. Two oscillators at fixed total energy give exact master evolution, an exact realization of this covariance shear, and the reduced symplectic limit. For the non-Abelian SL(2,$\R$) model we compute the coherent and Weyl master symbols, prove essential self-adjointness and a finite-time propagation estimate, and derive the spectral bottom $\hbar^2/2$.

The high-mass black hole population inferred from ground-based observations can substantially affect the number of binaries detectable by the Laser Interferometer Space Antenna (LISA). We use population constraints based on data from the latest LIGO/Virgo/KAGRA Gravitational-Wave Transient Catalog (GWTC-5.0), as well as constraints from the O3 search for intermediate-mass black hole binaries, to forecast the number and masses of binary black holes detectable by LISA. Using the released GWTC-5.0 population posterior, we obtain $6.6^{+5.5}_{-2.2}$ expected detections with signal-to-noise ratio $>8$ in 4 years (median and $90\%$ credible interval). The alternative population models we consider use a broken power law with two or three Gaussian peaks for either the primary-mass distribution or a common mass distribution for both black holes. For the three-peak model with the common mass distribution, extrapolating from $300$ to $1000M_\odot$ roughly doubles the median expected number of LISA detections to $\sim14$. The upper end of its $90\%$ credible interval rises from tens to thousands of expected detections, although approximations may limit the reliability of the most extreme counts. For the reference GWTC-5.0 population, $39^{+22}_{-11}\%$ of the binaries detectable by LISA merge during the mission or within $10$ years after its end and are potential multiband sources. Essentially all of these mergers would be detectable by a reference Cosmic Explorer configuration if it is operating at merger. Ground-based measurements of the high-mass population can therefore inform both LISA forecasts and the prospects for observing the same binaries through inspiral and merger.

The Emergent Universe scenario is based on the assumption that the universe originates from a past-eternal Einstein static (ES) state, subsequently evolving toward an inflationary phase and a hot Big Bang era. Such models are appealing as they provide nonsingular and geodesically complete cosmological histories. However, it has been argued by Mithani and Vilenkin that, even when the ES state is classically stable, certain models can admit semiclassical tunneling channels leading to quantum decay toward configurations of vanishing scale factor. In this work, we investigate the classical and semiclassical stability of the ES regime in the context of Jordan-Brans-Dicke (JBD) theory. We analyze the structure of the Wheeler-DeWitt potential in minisuperspace and study representative semiclassical tunneling channels compatible with the Hamiltonian constraint. We show that, for suitable choices of the JBD potential and model parameters, the ES configuration can be robust against both classical perturbations and the specific semiclassical tunneling channels analyzed in this work. Our results indicate that the quantum instability discussed by Mithani and Vilenkin may be avoided within certain regions of parameter space, while leaving open the possibility of more general tunneling processes beyond the scope of the present analysis.

We develop a geometric--analytic proof of the reverse isoperimetric inequality for compact AdS black hole horizons in Einstein gravity. At fixed thermodynamic volume, a York slice/Jacobi variation of the gravitational action shows that the spherical Schwarzschild--AdS solution is a strict local entropy maximum against generic non-spherical deformations. The finite global extension is formulated within the hypotheses of the Sherif--Dunsby (SD) rigidity theorem: compactness and spherical topology, the required intrinsic Ricci decomposition $\mathrm{Ric}_h=\alpha\,\mathbf e\!\otimes\!\mathbf e+\beta N$ with $\alpha\neq\beta$, a proper conformal transformation of the hypersurface metric given by $\widetilde h_{ab}=e^{2\varphi}h_{ab}$ that preserves its intrinsic scalar curvature, $\widetilde R\equiv R[\widetilde h]=R[h]\equiv R>0$, and negative sheet expansion. Compactness and $S^3$ topology are built into the class considered here. In the static spherical sector such as Schwarzschild--AdS and RN--AdS, the SD Ricci form is naturally realized while it is an additional restriction for Kerr--AdS case. For the $S^3$ topology, a positive Yamabe type conformal class exists for which the Yamabe theorem provides a representative of positive and constant scalar-curvature. We further restrict to the scalar-curvature preserving conformal transformation required by the SD theorem. The negative sheet expansion is obtained using gravitational focusing. Within this admissible class, a non-round Kerr--AdS horizon cannot maximize the entropy, while fixed thermodynamic volume selects the corresponding round Schwarzschild--AdS comparator. The analysis thus establishes a generic local entropy maximum and a finite global result within the stated geometric rigidity class, identifying the role of gravity in reversing the ordinary isoperimetric problem.

This work aims to present some quantum aspects of a non-commutative (NC) gauge gravity formulation of a Schwarzschild-like black hole constructed via the Moyal twist $\partial_t \wedge \partial_\theta$. Particle creation is estimated for bosonic and fermionic fields using the quantum tunneling method, with divergent integrals treated through the residue prescription. Since the surface gravity is well defined for this configuration, the corresponding emission rates and evaporation lifetimes are also computed. In addition, previously reported results in the literature on gauge gravity Schwarzschild black holes are revisited. Finally, we infer constraints on the NC parameter $\Theta$ from solar system tests.

Modified theories of gravity often introduce geometric structure beyond general relativity to address unresolved problems in the gravitational sector without invoking ad hoc matter fields. Mimetic gravity, for example, generates an effective cosmological dark sector by isolating the conformal mode of the metric, while Hořava--Lifshitz gravity attains power-counting renormalizability by endowing spacetime with a preferred dynamical foliation. Although chronology protection was not the original motivation for either theory, both can realize it classically through stable causality. This suggests that chronology protection itself may be elevated from a derived property to a guiding principle for constructing modified gravitational theories, especially if its implementation at the quantum-gravitational level leaves infrared imprints in the effective action. Motivated by this possibility, we introduce a toy metric--affine gravity model whose chronology-protecting sector is purely geometric. The model breaks projective invariance and selects a timelike, closed non-metricity one-form. In the globally exact sector, this one-form defines a time function, realizing stable causality through affine geometry. On the matter-free, spatially flat FLRW branch with non-compact slices, $\Lambda=0$, and positive chronology-sector density, the local quadratic gravitational spectrum contains the two tensor modes of GR and a single scalar mode. The scalar has positive kinetic energy but a gradient instability, $c_s^2=-2$, requiring stabilization before a viable cosmological application can be established. We investigate the classical cosmological effects and scalar-mode dynamics of this purely geometric chronology-protecting extension of general relativity.

We derive bounds on the lifetime of an evaporating black hole. The minimum lifetime bound follows from energy conservation and purification, within the framework of `asymptotically semiclassical spacetimes'. The recently derived expression for the Bondi flux of Hawking radiation, together with the expression for the entanglement entropy of Hawking radiation at null infinity, is used to investigate the purification phase after the last semiclassical ray. We discuss the energy-cost of entanglement purification and find a lower bound on the purification time of the black hole, which scales as $M_0^4/\hbar^{3/2}$, where $M_0$ is the initial black hole mass. Additionally, motivated by the Planck luminosity bound in quantum gravity, we include the additional assumption that a Planck mass black hole is metastable. With this assumption, the purification time is in fact exponential in the square of the initial black hole mass, $\tau\sim\sqrt{\hbar}\,\exp(\gamma M_0^2/\hbar)$ with $\gamma>0$, i.e., exponential in its initial area. We find that the redshift exponent is negative in this purification phase, which indicates the existence of a white-hole remnant that releases information slowly. We comment on phenomenological implications for primordial black hole remnants.

We introduce a new series decomposition of the waveform constructed in the spirit of Debye expansions in scattering theory, and we use this to analyse the time-domain response of compact, horizonless bodies to scalar-field perturbations on curved spacetimes. The Debye decomposition separates out direct exterior propagation, surface reflection, and successive transmissions through the interior of a compact body, and it provides an intuitive interpretation of the waveform in terms of geodesic trajectories. By analysing the quasinormal-mode (QNM) content of individual Debye terms, we set out a Debye-QNM description that is complementary to the standard QNM description. With this framework, we examine a scalar field propagating on two illustrative `Schwarzschild star' compact-body spacetimes: a neutron-star-like model $R>3M$ and an ultracompact object $R<3M$. We show that the closed-form Debye reconstruction matches well with the exact waveform, and that it converges even at early times, giving an accurate description of all waveform features including the prompt response. In the neutron-star case, the low-order Debye terms mainly describe the ringdown and a non-modal component associated with the sub-threshold branch cut. In the ultracompact case, the Debye series organizes the waveform into a prompt/ringdown contribution followed by a succession of echo-like wavepackets. The new Debye-QNM expansion and the standard QNM expansion have complementary spectral interpretations: the former identifies modes in individual propagation channels, whereas the latter describes collective resonances that are resummations of the former. This distinction clarifies how echo-like structures emerge from repeated interior propagation, and how pole and branch-cut contributions enter the time-domain signal.

We present a general construction of charged regular black holes as solutions of a generalization of the Einstein--Maxwell field equations in spherical symmetry in which the Einstein tensor is deformed into an identically conserved tensor containing up to second derivatives of the gravitational field. The generality of the construction allows us to define the field equations satisfied by generic regular black holes when becoming charged. The conditions that guarantee regularity of charged solutions are evaluated and shown to be more stringent than the regularity conditions for uncharged solutions. This implies, in particular, that the charged versions of the Bardeen and Hayward black holes become singular. Improved versions of the Bardeen and Hayward metrics that remain regular when charged are proposed. Our results indicate that regularizing the vacuum solutions of general relativity is, in general, not enough to yield regular solutions in other situations of physical interest. The implications that follow for the construction of realistic regular black holes, in which aspects such as rotation and the presence of matter fields are taken into account, are discussed.

The tidal deformability of a compact object is encoded in a single function of frequency, the retarded Green's function relating the induced multipole to the applied tide. Causality, reality, passivity, and the high-frequency conditions required for a positive-measure dispersion representation allow this response to be rescaled into a holomorphic self-map of the upper complex frequency half-plane. Using the Schwarz-Pick theorem, already employed to derive the quantum chaos bound in black hole physics, we provide a bound on the rate of the tidal response with respect to the frequency. For a neutron star with a positive tidal spectral threshold, the dynamical Love number is bounded in terms of the static response and the lowest frequency carrying nonzero tidal spectral weight, with the ideal single-mode model saturating the bound. For a black hole, whose tidal spectrum is gapless, the dynamical Love number is a finite-part moment of the horizon absorption spectrum. Under a growth hypothesis on the complete response the theorem constrains the full Euclidean response, but it does not bound the dynamical Love number.

We consider the Bessel-Hagen construction for linearised Weyl-squared gravity, whose action depends on the metric perturbation $h_{\mu\nu}$ through the linearised Weyl tensor $C^{(1)}_{\mu\nu\rho\sigma}$. This provides a curvature-based comparison with the Fierz-Pauli theory, in which the action contains first derivatives of $h_{\mu\nu}$ whereas the first local gauge-invariant field strength contains two, and the construction determines a gauge-invariant class of Noether currents without selecting a preferred gauge-invariant local energy-momentum tensor. Since the Weyl tensor is the irreducible spin-2 part of the curvature, it is of particular interest to ask whether an action built from it admits a local representative analogous to the Maxwell tensor. We show that the Bessel-Hagen construction extends to the conformal group, acting on the fields on a fixed Minkowski background, and yields a gauge-invariant conserved-current class for each generator. Nonetheless, no nonzero local, polynomial, symmetric rank-two tensor of mass dimension four, quadratic in $h_{\mu\nu}$ and with constant dimensionless coefficients and no explicit coordinate dependence, is both strictly invariant under the linearised diffeomorphism and Weyl gauge symmetries and conserved on the Bach shell. The gauge symmetries restrict such a tensor to depend on $C^{(1)}$ and its derivatives, while the dimension and field degree permit only terms quadratic in $C^{(1)}$ without further derivatives. Four-dimensional Weyl identities then reduce all candidates to pure traces, whose conservation requires their coefficients to vanish. Thus, building the action from a gauge-invariant curvature does not recover the electromagnetic result. A first-order gauge-covariant field strength may provide a route to such a representative, although its presence alone is not sufficient.

Hawking radiation sets stringent constraints on Primordial Black Holes (PBHs) as a dark matter candidate in the $M\sim 10^{16}$ g regime based on the evaporation products produced by the black hole, motivating the need to rigorously model the photon, electron, and positron emission spectra. This manuscript is the second in a series of two papers (see Vasquez et al. [Phys. Rev. D, 112:063002 (2025)] for the first paper in the series) with the goal of proving the stochastic emission of electrons and positrons, known as the "stochastic charge effect" and first predicted by Page [Phys. Rev. D, 16:2402 (1977)] using semi-classical arguments, arises from quantum electrodynamics (QED) on a Schwarzschild spacetime. We derive the corrections to the $e^\pm$ from the relevant term in the Hamiltonian (the long-range monopole: $H_{\rm int,0L}$) to first order in the fine structure constant ($\alpha$), and show that the semi-classical terms are also present in the QED calculation. We also highlight which terms in our analysis only appear within our quantum mechanical approach and cannot be explained otherwise. We find that due to some cancellation of terms, over the range of $2.2\times 10^{16}$ - $1.7\times 10^{17}$ g, the net correction to the $e^\pm$ emission rate is less than 2%, versus the suppression of up to 5% previously found by semi-classical arguments.

We study the thermodynamics of asymptotically flat five dimensional Einstein Gauss Bonnet black holes within the framework of the extended generalized uncertainty principle (EGUP). The geometry dependent localization scale is fixed by requiring the undeformed relation to reproduce the surface gravity temperature. The resulting expression consistently recovers the GUP, EUP, and semiclassical limits, while imposing a joint constraint on the minimum length and minimum momentum parameters. Due to the nonmonotonic behavior of the effective localization scale, the reality condition does not generically yield a unique minimum horizon radius. Depending on the parameter values, the admissible domain may remain connected, develop a degenerate critical radius, or split into two disconnected branches. We derive the entropy, heat capacity, and Helmholtz free energy, and analyze their behavior numerically. The Gauss Bonnet coupling shifts and suppresses the near horizon temperature maximum, whereas the EUP sector induces a temperature minimum followed by linear growth at large radius. In the two branch regime, the outer endpoint exhibits finite temperature and vanishing heat capacity but is approached from the locally unstable side, and should therefore be interpreted as a limiting thermodynamic configuration rather than a dynamically established remnant. Finally, we show that the perturbative entropy deviates from the exact result at large radius, and that the leading GUP entropy correction persists in the Einstein gravity limit.

This dissertation investigates scalar field descriptions of the dark sector (of the Universe), with emphasis on scalar-tensor cosmology, inflationary effective field theory, quintessence, and ekpyrotic/cyclic alternatives to inflation. The thesis first reviews scalar-tensor theories of gravity, starting from Brans-Dicke theory and extending to general non-minimally coupled scalar fields. Particular attention is paid to the interpretation of the scalar field, the relation between the Jordan and Einstein conformal frames, and the role of conformal transformations in cosmology. This provides the theoretical basis for treating scalar fields either as modified matter or as additional gravitational degrees of freedom. The second part discusses cosmological inflation from the viewpoint of effective field theory. The spontaneous breaking of time translations, the Goldstone description of adiabatic perturbations, higher-dimensional operators, radiative corrections and Planck-suppressed terms are analyzed in the context of ultraviolet sensitivity and the eta problem. The third part is devoted to quintessence as the simplest dynamical dark energy model. 'Tracking', 'scaling', 'thawing' and 'freezing' behaviors are discussed, together with observational diagnostics such as the statefinder parameters, the $(\omega_{\phi},\omega'_{\phi})$ plane and the $Om(z)$ diagnostic. The DESI DR2 results are used as motivation for considering time-dependent effective dark energy beyond a strict cosmological constant. The final part studies ekpyrotic and cyclic cosmologies. The ekpyrotic phase is analyzed as a smoothing mechanism based on an ultra-stiff scalar field equation of state. Perturbations, non-Gaussianity, tensor modes, bounce conditions, entropy production, geodesic incompleteness and phase-resolved field-space distance bounds are discussed.

Exceptional points (EPs) and eigenstate hysteresis, previously found in Kerr only with an auxiliary scalar field, arise intrinsically in the quasinormal-mode spectrum of Kerr-Newman black holes. Using a hyperboloidal formulation of the coupled gravito-electromagnetic Teukolsky equations and a Chebyshev pseudospectral method, we compute the $\ell=m=2$ spectrum and locate four EPs at up to $99.974\%$ of extremality, one from a new repulsion. The gaps close as a square root branch point, and quasistatic loops around one or more EPs exchange the coalescing modes, confirming hysteresis.

We construct a unified (quantum) description, by the gauge principle, of gravity and Standard Model (SM), that generalises the Dirac-Born-Infeld action to the SM and Weyl geometry, hereafter called Weyl-Dirac-Born-Infeld action (WDBI). The theory is formulated in $d =4-2\epsilon$ dimensions. The WDBI action is a general gauge theory of SM and Weyl group (of dilatations and Poincaré symmetry), in the Weyl gauge covariant (metric!) formulation of Weyl geometry. The theory is SM and Weyl gauge invariant in $d=4-2\epsilon$ dimensions and there is no Weyl anomaly. The WDBI action has the unique elegant feature, not present in other gauge theories or even in string theory, that it is mathematically well-defined in $d=4-2\epsilon$ dimensions with no need to introduce in the action a UV regulator scale or field. This action actually {\it predicts} that gravity, through (Weyl covariant) space-time curvature $\hat R$, acts as UV regulator of both SM and gravity in $d=4$. A series expansion of the WDBI action (in dimensionless couplings) recovers in the leading order a Weyl gauge invariant version of SM and the Weyl (gauge theory of) quadratic gravity. The SM and Einstein-Hilbert gravity are recovered in the Stueckelberg broken phase of Weyl gauge symmetry, which restores Riemannian geometry below Planck scale. Sub-leading orders are suppressed by powers of (dimensionless) gravitational coupling ($\xi$) of Weyl quadratic gravity.

Black bounce spacetime, proposed by Simpson and Visser (SV), can describe the Schwarzschild solution, regular black holes, and traversable wormholes in a unified manner, depending on the value of the regularization parameter $a$. This paper primarily explores the dynamics of charged particle in the magnetized SV spacetime, and constrains the parameters of the SV spacetime along with its surrounding magnetic fields. The constraints are given by using $\chi^2$ analysis combined with high-frequency quasi-periodic oscillation (HFQPO) data observed from three microquasars: GRS 1915+105, XTE 1550-564, and GRO 1655-40. The results indicate that the magnetic field significantly influences the position of the innermost stable circular orbit of charged particle and frequency distribution of epicyclic motion, which excites more resonance model variants, enhancing observational effects. Additionally, we employ the Akaike Information Criterion (AIC) to evaluate resonance model and its various variants. The support for different models from observational data shows significant variation: $E R_8$ as the best model is supported strongly, $ER_3$ model has moderate evidence of support, $ER_6$ and $ER_7$ models are considerably less support, while other resonance models have essentially no support. The result from AIC is broadly consistent with the results obtained from the Bayesian Information Criterion (BIC) and the Bayes factor. For models more supported by the observational data, the allowed ranges of the regularization parameter: $0\leq a/M<0.736$ ($68\%$ confidence level) suggests that HFQPOs data could support the magnetized black bounce spacetime as a regular black hole, and the smaller value of the regularization parameter indicates a possibility of the presence of quantum effects.

With the release of the Gravitational-Wave Transient Catalog GWTC-4.0 by the LIGO-Virgo-KAGRA (LVK) collaboration, 218 candidate detections of gravitational waves (GWs) from compact binary coalescences (CBCs) have been reported. This milestone represents a major advancement for GW cosmology, as many methods, particularly those employing the spectral siren approach, critically depend on the number of available sources. We investigate the impact of a novel parametric model describing the full population mass spectrum of CBCs on the estimation of the Hubble constant. This model is designed to test the impact of heavy black holes in GW cosmology. We perform a joint inference of cosmological and population parameters using 142 CBCs from GWTC-4.0 with a false alarm rate smaller than 0.25 per year, using both spectral and dark siren approaches. With spectral sirens, we estimate the Hubble constant to be $H_0 = 78.8^{+19.0}_{-15.3}\,{\rm km s^{-1} Mpc^{-1}}$ (68% CL), while the dark siren method yields $H_0 = 82.5^{+16.8}_{-14.3}\,{\rm km s^{-1} Mpc^{-1}}$ (68% CL). These results improve the uncertainty by approximately 30.4% and 36.2%, respectively. We show that this improvement is linked to the presence of a new mass scale in the binary black hole mass spectrum at $63.3^{+4.8}_{-4.8}\,M_{\odot}$, which provides additional constraints on the Hubble constant. Besides providing the tightest standard-siren constraints on $H_0$, this highlights the importance of a heavy-mass feature in the black hole spectrum.

The generation of accurate waveforms from binary black hole (BBH) mergers is a major effort in Gravitational-Wave Astronomy. In recent years, machine-learning-based surrogate models for BBH waveforms have been proposed. Those offer the potential to dramatically accelerate waveform generation while maintaining accuracy competitive with that of traditional waveform approximants. In this work, we investigate the viability of autoencoders as generative models for gravitational-wave signals from quasi-circular BBH mergers. We introduce AESur3dq8, a novel surrogate waveform model based on autoencoders that enables the rapid and accurate construction of large template banks, producing millions of waveforms in under a second using modest computational resources. The model is trained on the numerical-relativity-informed surrogate NRHybSur3dq8 and subsequently fine-tuned using the SXS catalog of BBH simulations. We demonstrate that waveforms generated by AESur3dq8 achieve mismatches of order $10^{-4}$ with respect to Numerical Relativity waveforms, and that parameter estimation performed with these templates yields results fully consistent with those reported by the LIGO-Virgo-KAGRA Collaboration for observed gravitational-wave events.

We advocate for a holographic definition of thermodynamic pressure and volume for black holes based on quasi-local gravitational thermodynamics. When a black hole is enclosed by a finite timelike boundary, York's quasi-local first law includes a surface pressure conjugate to the boundary area. Assuming the existence of a holographically dual theory living on this boundary, these geometric quantities correspond to the pressure and volume of the dual thermal system. In this work we focus on static, spherically symmetric black holes, for which these quantities reduce to global thermodynamic variables. The holographic volume provides a notion of system size, allowing extensivity to be defined in standard thermodynamic terms, and it yields a definition of the large-system limit. For the asymptotically flat case, we show that, in the canonical thermodynamic representation, small Schwarzschild black holes are non-extensive, whereas large black holes become extensive in the large-system limit. A similar conclusion applies to Anti-de-Sitter Schwarzschild black holes, with the difference that the quasi-local energy of the large black hole also becomes extensive in the large-system limit. Before this limit, the energy decomposes into subextensive and extensive contributions, and we derive an explicit expression for the extensive part as a function of the finite volume and entropy.

Lunar gravitational-wave (GW) detectors relying on the measurement of the response of the Moon to GWs are susceptible to a seismic background, which might pose a fundamental sensitivity limitation. The Lunar Gravitational-wave Antenna (LGWA) was conceived as an array of accelerometers with the idea that data can be processed to distinguish between a GW signal and the seismic background. As a result, the seismic noise of the GW measurement would be mitigated. However, so far, no quantitative assessment of the mitigation of the seismic background has been provided. In this article, we derive the analytical expressions for the optimal squared signal-to-noise ratio for a two-station array in an isotropic, random, Gaussian seismic field. Our numerical analysis reveals that the capacity to mitigate the seismic noise critically depends on the distance between the two stations relative to the seismic-correlation length. We demonstrate that optimal placement of the two stations can yield significant improvements in the equivalent seismic noise amplitude spectral density (ASD), approximately a factor of 2.3 at 0.3 Hz, compared to the measurement with a single station in the seismic-noise-dominated limit. The equivalent ASD of the seismic noise also exhibits distinct oscillatory and mitigation features arising from the Bessel-function structure of the noise correlation.

We elucidate the physical nature of ghosts above the multi-particle threshold by contrasting them with unstable particles in quantum field theory. We first consider the asymptotic formulation, where ordinary positive-norm one-particle states can be unstable and decay, whereas ghosts survive asymptotically without decaying, yet admit no particle interpretation due to interference with the multi-particle component which masks the negative-norm one-particle state. This distinction originates from two different analytic structures of the dressed propagator, whose complex conjugate poles lie on the first or second Riemann sheet in the ghost or ordinary case, respectively. Ghost resonances are, in principle, phenomenologically distinguishable from ordinary ones, being narrower and exhibiting weaker interference between positive- and negative-energy peaks. We then formulate the quantum field theory in a finite interval of time and, working within a suitable approximation for the dressed propagator, find that finite-time effects amplify differences in the resonant behavior and give rise to new features, such as higher peaks in ghost resonances. Distinct temporal regimes are also identified: for times shorter than the inverse width, an approximate free-particle description is valid; at later times interactions and interference dominate, leading to decay or multi-particle masking. This study supports the absence of freely propagating ghost particles in the asymptotic limit.

When stochastic field dynamics are cast into a path-integral formulation, perturbation theory becomes systematic but the resulting expansion quickly grows combinatorially large. The setting targeted here includes fields with several components and several dimensions, matrix propagators, tensor-valued couplings, and non-Gaussian driving noise specified by arbitrary n-point cumulants. Wick pairings grow factorially, and component indices must be routed through the tensor-valued vertices. The useful output is not a raw contraction list, but a diagram table: one entry per topology, with multiplicities, coupling sums, signs, and causal constraints resolved. We present sft-wick, an open-source Python package that constructs these diagram tables and computes their integrals numerically. Given an action and an observable, it enumerates topologically distinct Feynman diagrams, derives their algebraic coefficients, and evaluates the resulting diagram integrals from user-supplied response and cumulant functions. The core algorithm enumerates spatial topologies before routing component indices, avoiding contraction-by-contraction Wick expansion. Response-field constraints, including vanishing response-response contractions, the Ito prescription, and the absence of causal response loops, are enforced during enumeration. Predictions are validated against direct Langevin simulations in two worked examples, with Gaussian and with non-Gaussian driving noise, and agree with the simulations within stated error budgets.

In this paper we study the dynamics of relativistic detonation waves theoretically and numerically. The reaction is physically accounted for by an extra term in the definition of the total energy density and by an additional equation for the evolution of the mass fraction of the reactant, while leaving formally unmodified the equations of mass and energy-momentum conservation. In this way, the Rankine-Hugoniot relations maintain the same formal structure of the inert version. For the numerical solution we use a finite volume ALE scheme with a second order TVD space-time reconstruction for the homogeneous part of the system, where the mesh velocity is chosen equal to the shock speed, and we combine it through operator splitting with a locally implicit algorithm for the potentially stiff reaction source terms that arise in the equation of the reactant. We furthermore propose a particularly efficient algorithm for the conversion from the conserved to the primitive variables, which for the relativistic Euler equations is known to be nontrivial. Following this approach, we can successfully solve the Zel'dovich-von Neumann-Doering profile of a relativistic detonation wave, up to Lorentz factors of the shock front $\gamma_s\sim 7$. Our analysis allowed us to highlight a new special relativistic effect, which has remained unnoticed so far. While in Newtonian detonations the Zel'dovich pressure jump decreases monotonically with the mass flux through the shock front, in the relativistic case it shows a minimum and then rises monotonically as a function of the mass flux. This may have interesting physical implications on the amount of energy that can be extracted from a relativistic detonation wave.

While the standard $\Lambda$CDM paradigm is in excellent agreement with most current cosmological observations, theoretical challenges surrounding the cosmological constant ($\Lambda$) have strongly motivated the exploration of dynamical dark energy (DE) and modified gravity (MG) models. Investigating the physical nature of the cosmic acceleration requires N-body simulations to probe the non-linear growth of cosmic structure and prepare for the high-precision data from Stage-IV surveys. In this paper, we present EFT-RAMSES, a comprehensive extension of the ECOSMOG cosmological simulation code designed to explore non-linear structure formation in DE and MG scenarios. We embed the effective field theory of dark energy (EFTofDE) framework into this new numerical pipeline, utilising the $\alpha$-basis parameterisation to provide a versatile, model-agnostic, computational engine. By consolidating diverse scalar and vector-tensor theories---including the normal and self-accelerating Dvali-Gabadadze-Porrati (DGP) models, cubic Galileons (cubic scalar Galileon (csG), cubic vector Galileon (cvG) and generalised cubic covariant Galileon (GCCG)), and generic effective field theory (EFT) parameterisation---into a single "master" Vainshtein equation, this pipeline bypasses the need for model-specific solvers and easily specialises to any particular model. As validations, we perform high-resolution N-body simulations for the normal-branch DGP (nDGP), csG, GCCG, and EFT models, comparing the resulting matter power spectra against dependent and independent codes such as legacy ECOSMOG and HiCOLA, as well as linear theory, and find excellent agreement. EFT-RAMSES provides a robust and versatile computational tool for precision cosmological tests of DE and MG using upcoming cosmological surveys. The code is available for download from the GitHub EFT-RAMSES repository.

We consider the extension of the $\delta$-shift connecting Tr$(\phi^3)$ and pion amplitudes to observables in cosmology. We start in flat-space and explain how one can extract the pion wavefunction and correlators from those of Tr$(\phi^3)$ theory, via a simple kinematic deformation. As opposed to the amplitude, the $\delta$-shift for the wavefunction is no longer a linear deformation on the kinematics since the wavefunction depends on magnitudes rather than the squares of momenta. We "linearize" this deformation by using the frequency representation - allowing us to recast the contribution from any graph as a sum over residues. We then show how this construction extends to de Sitter, and find that, remarkably, in the frequency representation, the pion de Sitter wavefunction and correlators can be formulated in precisely the same way as in flat-space. Amongst other things, this unified formulation reveals a simple universal soft-limit for flat-space and de Sitter, where, in the soft-limit, the wavefunction turns into a sum of wavefunctions in a mixed theory of pions and scalars.