Papers

We study the inflationary no-boundary wavefunction in a “linear-roll limit,” in which $G_N \to 0$ while the Hubble scale $H$ and the slope of the inflaton potential are held fixed. Although bulk graviton fluctuations are suppressed in this limit, quantum inflaton fluctuations remain finite. Because reheating occurs on a surface of fixed inflaton value, these fluctuations become fluctuations of the conformal factor of the reheating metric. The probability measure for these fluctuations simplifies drastically and becomes Gaussian, even for large fluctuations. The resulting log-correlated theory at superhorizon scales is a $d$-dimensional analog of Liouville gravity without the exponential potential, which we call Logarithmic Gravity. The quadratic and linear terms are determined by conformally covariant scattering data; in even dimensions we relate them to the critical GJMS operator and Branson $Q$-curvature. From bulk unitarity, we argue that one-loop effects do not generate additional conformal-factor dependence in the physical probability measure, and we verify the cancellation explicitly in $2 + 1$ dimensions. For the no-boundary norm with a rolling inflaton, we show that the noncompact residual conformal symmetries can be gauge fixed with a finite Faddeev-Popov determinant, so they do not force the sphere contribution to vanish. In addition, conditioning on the absence of vacuum decay by bubble nucleation generates the Liouville exponential potential in the probability measure.

We analyze circular-orbit stability, epicyclic resonances, relativistic precession, and quasi-periodic-oscillation (QPO) constraints in the constant-curvature vacuum sector of metric $f(R)$ gravity. The Schwarzschild–(anti-)de~Sitter and Kerr–(anti-)de~Sitter backgrounds are characterized by curvature $R_0$ satisfying the algebraic trace equation. We derive stationary-coordinate-time orbital and epicyclic frequencies and determine stable timelike circular-orbit domains. Positive curvature confines stable motion between innermost and outermost stable circular orbits, which merge at a critical curvature, and permits two resonance radii for suitable frequency ratios. Negative curvature allows stable motion to arbitrarily large radii, with $\Omega_\theta/\Omega_r\rightarrow1/2$, compared with unity in the asymptotically flat limit. We determine the $3{:}2$, $2{:}1$, and $3{:}1$ resonance branches and signed nodal precession, recovering the Lense–Thirring limit. We also evaluate angular-momentum-weighted rigid-flow precession and viscous alignment, with the outermost stable orbit bounding positive-curvature flows. A Bayesian Markov chain Monte Carlo analysis combining the simultaneous GRO J1655–40 QPO triplet with an independent dynamical-mass measurement yields $R_0M^2=-5.57^{+12.94}_{-16.15}\times10^{-4}$ at $68\%$ credibility, conditional on the geodesic relativistic-precession prescription and adopted time normalization. Kerr remains allowed, with negligible fit improvement from nonzero curvature. Doubling the mass uncertainty broadens the curvature interval by approximately $2.1$; removing the mass likelihood reveals an extended, prior-dependent degeneracy. This is therefore a joint QPO and dynamical-mass constraint, with no significant evidence for departure from Kerr.

We study the massive scalar quasinormal-mode spectral problem on a Schwarzschild background using an extended Chebyshev spectral method. The massive dispersion relation has a two-sheeted analytic structure, which we uniformise before discretisation. This converts the radial problem into a seventh-degree polynomial eigenvalue problem while incorporating the quasinormal-mode boundary conditions at the horizon and spatial infinity. The method yields stable spectra for low multipoles, high overtones, and frequencies on both sides of the nominal mass threshold, including regimes in which WKB and continued-fraction approaches become difficult to apply. For complex frequencies, the far-field behaviour cannot be classified from the real part of the frequency alone, but depends on the complex wavenumber and its Riemann sheet. We also identify stable families of purely imaginary roots with approximately uniform spacing in their damping rates, whose physical interpretation remains open. The Schwarzschild scalar problem is intended as a controlled benchmark for massive-field quasinormal-mode calculations rather than as a direct model of tensorial Kerr ringdown.

X-ray pulse-profile modeling can measure neutron-star radii, but its physical interpretation remains limited by the largely phenomenological description of the surface hotspots. Here we connect the X-ray hotspots directly to the pulsar magnetospheric structure and jointly infer the mass, radius, and magnetic geometry of the massive millisecond pulsar PSR J0740+6620 from NICER and XMM-Newton observations. Using a GPU-accelerated implementation, we compare two low-dimensional magnetic configurations that can produce non-antipodal emission: a centered axisymmetric dipole–quadrupole and a shifted dipole. The shifted-dipole model is decisively favored under the adopted priors, with $\Delta\ln Z=5.65$ (Bayes factor $\sim285$), and yields $M=2.059^{+0.068}_{-0.069}\,M_{\odot}$ and $R=13.28^{+1.47}_{-1.07}\,\mathrm{km}$, broadly consistent with previous phenomenological analyses, while requiring nearly symmetric heating of the two polar caps. Both the marginalized shifted-dipole posterior and the timing-compatible representative require an effective X-ray-emitting footprint much smaller than the nominal force-free polar cap calibrated for a centered dipole. This compact footprint is not reproduced by our exploratory photon-conversion estimates and instead points to missing physics in the mapping from magnetospheric currents to observable X-ray emission. Our results show that physically motivated hotspots can preserve the mass–radius inference while turning hotspot morphology into a probe of pulsar magnetospheric structure and emission physics.

We study heavy-heavy-light-light correlators in holographic CFTs when the heavy operator is dual to a compact object localized on scales much smaller than the AdS radius. In the long-wavelength regime, the internal structure of the heavy state is described by a worldline effective field theory, whose local operators encode finite-size response coefficients such as tidal Love numbers. Focusing on weakly self-gravitating objects, we show that the Witten diagrams generated by local heavy-light interactions reorganize into the Born series of an effective wave equation for the light bulk field. We reproduce the same correlator by solving this wave equation with localized interactions and identify how the worldline Wilson coefficients are encoded in the CFT data. Our results provide a direct relation between the finite-size response of compact objects in AdS and the dimensions and OPE coefficients of heavy-light and light-light composite operators in the dual CFT.

More general boundary conditions are introduced - with respect to known literature - which produce a well-posed stationary action principle in $f(R)$ gravity. These conditions encompass the known cases, thus enlarging the space of admissible solutions. The corresponding Gibbons-Hawking-York boundary terms are explicitly computed and hold for any analytic f(R). The perspectives of application concerning the scalar-tensor mapping and the laws of black-hole thermodynamics are outlined in the conclusions.

A controlled correspondence is established between reduced relational dynamics and extended constrained quantization in an FLRW cosmology coupled to a Schutz perfect fluid. A canonical transformation in the matter sector yields a deparametrized constraint of the form $\mathcal C=p_T+H$, with $T$ serving as an internal time. In the extended Weyl–Wigner formulation, the quantum constraint is imposed bilaterally. Its antisymmetric part gives the exact Moyal evolution generated by the reduced Hamiltonian, while its symmetric part imposes an independent quantum shell condition. For a fixed self-adjoint realization of $\hat H$, every reduced density operator supported on its negative spectral subspace admits an explicit distributional extension. A spectral dyad with energies $E$ and $E'$ is mapped to a clock Wigner distribution supported at $p_T=-(E+E')/2$, with relational phase determined by $E-E'$. The map preserves off-diagonal coherences, satisfies both star constraints, and has the reduced Wigner state as its $p_T$ marginal; it is therefore injective on the admissible positive-density sector. A flat dust model with $q=1/2$ and Dirichlet data provides an explicit example: its reduced spectrum is $(-\infty,0]$, so the admissible sector contains all normalizable reduced states. The correspondence applies to a fixed constraint representative and quantum realization.

We show that inflation with a large number of fields, as predicted by concrete ultraviolet embeddings, generically produces almost-local cosmological collider signals in the bispectrum squeezed limit. We construct the most general boost-breaking mixings between the curvature perturbation and $N_{\rm f}$ additional fields, and extract the late-time scaling dimensions that dictate the soft limits of cosmological correlators. For a handful of fields, an enhanced squeezed limit (with potential oscillations) is a fine-tuned signal. At large $N_{\rm f}\sim100$, however, mixings generically drive the scaling dimensions toward the unitarity boundary. We show that this is a direct consequence of extreme value statistics and random-matrix universality, turning an almost-local bispectrum shape into a generic prediction for almost any masses and mixings.

We construct a five-dimensional generalization of the swirling universe and embed in it the Myers-Perry black hole and the rotating black ring. We prove that both solutions are free of conical singularities, analyze their geometrical properties, compute their mass and angular momentum, and discuss their uniqueness.

Recent baryon acoustic oscillation measurements from the Dark Energy Spectroscopic Instrument (DESI), combined with supernova observations, show a mild preference for an evolving dark-energy equation of state, in which dark energy remains phantom-like at higher redshift while a transition toward the quintessence regime emerges around $z\lesssim0.5$. Beyond the monotonic evolution of the equation of state, an oscillatory dark-energy scenario provides a potential alternative realization of dynamical dark energy. We study such an oscillatory scenario within the Einstein-scalar-Gauss-Bonnet gravity framework, where a scalar field with a hybrid exponential-quadratic potential couples nonminimally to the Gauss-Bonnet (GB) invariant. We choose a Gaussian GB coupling function localized around the minimum of the potential. During the late-time epoch, the field thereby oscillates around the potential minimum and eventually exits toward a stable de Sitter attractor phase. In the minimally coupled limit, the effective equation of state oscillates in the quintessence regime at low redshift, $z\sim0$, without crossing the phantom divide. The nonminimal coupling amplifies the oscillations and drives the effective equation of state across the phantom divide multiple times. Although a sufficiently strong coupling can induce negative scalar and tensor sound speeds, rendering the perturbation modes unstable. We identify a region of parameter space in which the model undergoes multiple phantom crossings while remaining free of ghost and gradient instabilities and approaching a stable de Sitter attractor in the future.

We prove that (n + 1)-dimensional de Sitter spacetime is locally the unique $(\Lambda > 0)$-vacuum spacetime whose Killing horizons intersect the conformal boundary $\mathscr{I}$. The intersection occurs at the isolated essential zeros of the extension of the Killing vector field to $\mathscr{I}$. We then reconstruct all de Sitter Killing vector fields from their boundary value and obtain a characterization of those admitting a Killing horizon in terms of a conformal invariant $\sigma$: $\sigma<0$ characterizes non-degenerate bifurcate horizons, whereas $\sigma = 0$ yields degenerate non-bifurcate horizons. Finally, we derive an intrinsic, conformally invariant formula for the surface gravity of the horizons in de Sitter, $\kappa^2 = |\sigma|$.

Interpretation of compact binary signals observed by third-generation gravitational-wave detectors is complicated by their high signal-to-noise ratios, often reaching hundreds to thousands, and by time- and frequency-dependent detector responses arising from Earth's rotation and the detectors' large physical extent. Building on prior work for LISA, we implement generic, robust extensions of the RIFT parameter estimation pipeline that enable interpretation of these sources using any existing waveform model, without recourse to intermediate pretrained data products like reduced-order approximations or normalizing flows. We demonstrate end-to-end recovery of finite-size binary-neutron-star injections in a three-site next-generation network to $\mathrm{SNR}=1000$, localizing the source's extrinsic parameters to $0.8\times10^{-3}\,\mathrm{deg}^2$ in minutes on a single GPU.

The kink soliton provides a simple construction of a topological thick 3-brane sourced by a minimally coupled canonical scalar field in five-dimensional general relativity. Although the flat-space kink is a solution of $\varphi^4$ theory, the gravitating configuration requires $M_*$-suppressed $\varphi^6$ corrections to support a stable warped geometry. Unlike its flat-space counterpart, the scalar perturbation spectrum contains no normalizable bound state. We nevertheless identify a single quasi-bound, or resonant, mode. Using a time-independent relative-probability analysis, direct time evolution, and a four-turning-point WKB calculation, we establish a direct connection between this resonance and the massive bound shape mode of the flat-space $\varphi^4$ kink. We also show that, within an EFT-consistent parameter window, the resonance can transfer energy from bulk geometric fluctuations to localized matter, thereby allowing the possibility of high-scale reheating in the early universe.

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.

The two-fluid model provides a powerful phenomenological framework for superfluids, where components interact through vortex-induced mutual friction. Quantum turbulence in such coupled two-fluid systems has become a central theme in low-temperature physics. However, the fundamental incompatibility between discrete vortex-line and continuum descriptions has historically forced reliance on phenomenological parameters. Here, we present an ab initio holographic simulation of this active two-fluid dynamics. Using a fully backreacted gravitational model, we intrinsically incorporate reciprocal momentum exchange and finite-temperature dissipation without empirical inputs. Contrasting continuously driven and freely decaying turbulence, we uncover pronounced non-Gaussian tails and spatial anisotropy in the normal-fluid velocity statistics, arising directly from the dynamical quantized vortex backreaction. Raising the temperature suppresses normal-fluid velocity fluctuations despite increasing the vortex density. This suppression is unambiguously traced to the thermal depletion of the superfluid condensate. Our results establish holographic duality as a rigorous first-principles framework for quantum turbulence, revealing the active role of the normal fluid far from equilibrium and yielding predictions for ongoing cold-atom and superfluid experiments.

Long-duration gravitational-wave (GW) inference inevitably encounters data gaps, which are often accompanied by abrupt, non-stationary changes in the detector noise power spectral density (PSD). Conventional practice typically analyzes the pre-gap and post-gap data separately, causing avoidable information loss and potentially degrading parameter inference. We build on Bayesian gap augmentation in the Wilson–Daubechies–Meyer (WDM) time–frequency domain and focus on a practically important failure mode: short gaps with large PSD amplitude jumps. In this regime, the local diagonal (Whittle-like) approximation that underpins the WDM likelihood can no longer be relied upon in the time direction near the gap edges, which may lead to biased and/or less robust inference unless the local diagonal validity is restored without resorting to full segmentation. We propose a two-stage, validity-driven remedy. First, frequency-domain prior-predictive prewhitening (PW) incorporates endpoint-informed noise information to mitigate the dominant mismatch responsible for poor diagonal behavior, enabling a more favorable WDM representation while retaining computational tractability. Second, when a time-direction smoothness criterion still fails, we apply adaptive gap expanding (AGE), selectively enlarging only the minimal neighborhood around the gap boundaries needed to restore local diagonal validity. Toy-model simulations with chimeric PSD transitions show that WDM+PW+AGE yields substantially tighter and more accurate posteriors than single-sided pre-gap/post-gap analyses, while maintaining computational efficiency suitable for next-generation missions.

Dense dark matter spikes around massive black holes (MBHs) have been widely predicted to produce gravitational-wave dephasing in extreme-mass-ratio inspirals (EMRIs) that are potentially observable by LISA. We show that EMRIs, the very objects used to probe these spikes, also destroy them. Combining Fokker-Planck models of nuclear star clusters with post-Newtonian three-body simulations of EMRI-dark matter encounters, we demonstrate that repeated gravitational slingshots irreversibly eject dark matter particles from the cluster's loss cone over gigayear time-scales. For MBHs at $z = 3$ with masses $\lesssim 10^5 \,M_\odot$, even conservative EMRI rates of $\mathcal{O}(1-10) \, \mathrm{Gyr}^{-1}$ suffice to deplete the spike density by orders of magnitude; for more realistic rates of $\mathcal{O}(100-300) \, \mathrm{Gyr}^{-1}$, the mass range extends to $\lesssim 10^6 \,M_\odot$. As a result, the gravitational-wave dephasing expected from such systems is greatly reduced, narrowing the prospects of detecting DM through this channel. Only heavy, high-redshift systems with sufficiently low EMRI rates – for example, a $\sim 10^6 \,M_\odot$ MBH at $z \gtrsim 5$ with $\lesssim 100$ EMRIs per Gyr – can induce dephasing that exceeds one radian.

The EPRL-FK spinfoam model in its semiclassical regime at fixed discretization faces a big limitation: its dominant configurations describe only flat geometries. We ask what additional condition is needed for the variational principle to reproduce the equations of motion of Regge calculus, the standard discretization of General Relativity. We recast the EPRL-FK model in wedge-holonomy variables and identify geometric closure as the missing condition. We prove that imposing geometric closure as an additional constraint alongside local flatness allows us to reconstruct curved geometries. On a regular, nondegenerate Lorentzian branch with spacelike tetrahedra, modulo gauge, they define a constraint surface equivalent to the space of length-Regge geometries. The wedge action restricted to this surface becomes the Regge action, and its tangent variations yield the length-Regge equations. Finally, we propose a way to implement geometric closure directly in the spinfoam amplitude. With this additional constraint, the EPRL-FK model is therefore equivalent to Regge calculus in its semiclassical regime.

Partially entangled thermal states (PETS) provide semiclassical families of black-hole microstates prepared through heavy shell insertions. We extend this shell-state framework and propose three-boundary partially entangled thermal states (PETS$_3$) by replacing the two-index insertion data with a trivalent junction tensor. The corresponding bulk three-boundary booklet geometry is constrained semiclassically by the Israel junction condition, allowing us to identify candidate symmetric and mixed-orientation branches. We verify the self-consistency of this construction by counting states in the symmetric all-black-hole sector. Using a heavy-operator probe, we further estimate the detection-to-universal ratio to be $Z_D/Z_U \simeq 3$, twice the two-boundary value of $3/2$. These results suggest that a fine-tuned probe localized on one boundary can test the proposed three-boundary shell state and potentially distinguish it from its two-boundary counterpart.

Coleman–De Luccia tunneling can exhibit an infinite tower of rapidly oscillating negative modes, complicating the semiclassical evaluation of the path integral. We show that this tower does not represent infinitely many bounce-specific instabilities, but instead is tied to a single underlying gravitational conformal sector. This sector is exposed in two different ways: by a large scalar gradient near the bubble wall and by the turning point of a compact Euclidean geometry. The corresponding conformal sector is already present in fluctuations about the false vacuum. Treating the bounce and the false vacuum in the same well-defined gauge and with a common regulator, we find that their high-frequency negative spectra approach one another. The ultraviolet tower therefore cancels from the relative negative-mode count, leaving a single bounce-specific negative mode. This finite-backreaction spectral cancellation provides a corresponding picture of the result obtained in the small-backreaction limit.

Extreme-mass-ratio inspirals (EMRIs) provide a promising probe of the dark matter environment surrounding massive black holes through their long-duration gravitational-wave signals. In this work, we investigate the influence of self-interacting dark matter (SIDM) on EMRI dynamics and gravitational-wave phase evolution. Motivated by the collisional Boltzmann description of SIDM, we construct a leading-order effective correction to the conventional Chandrasekhar dynamical-friction force, controlled by the momentum-transfer cross section $\sigma_T$ and the dimensionless collisionality parameter $n_\chi\sigma_T r=r/\lambda_{\rm mfp}$. We then compute the resulting orbital evolution, waveform modification, and accumulated gravitational-wave dephasing. In the enhanced-drag regime considered here, increasing the SIDM self-interaction strength increases the effective dynamical friction, accelerates the inspiral, and produces a progressively larger phase deviation relative to the collisionless dark matter case. We further distinguish the total dark-matter-induced dephasing relative to vacuum from the additional phase correction generated specifically by dark matter self-interactions. Our results demonstrate that the cumulative gravitational-wave phase of EMRIs can be sensitive to the microscopic momentum-transfer properties of dark matter, suggesting that future space-based detectors such as LISA may provide a complementary probe of SIDM in the vicinity of massive black holes.

Extreme-mass-ratio inspirals (EMRIs) offer a powerful probe of additional fundamental fields through their cumulative influence on gravitational-wave phases. However, modeling vector radiation from generic Kerr orbits requires the evolution of the Carter constant, which cannot be determined from energy and angular-momentum balance alone. Here we derive the orbit-averaged electromagnetic Carter-constant flux for eccentric and inclined, nonresonant Kerr geodesics, including sections at infinity and event horizon. Combining the gravitational and electromagnetic energy and angular-momentum fluxes, we construct generic adiabatic inspirals using a four-dimensional Chebyshev interpolation mathod. We incorporate the relativistic trajectories into the state of the art of FastEMRIWaveform package and perform Bayesian inference of vector charge carried by secondaries. Our analysis reveals substantial correlations between the charge and intrinsic source parameters, with vector charge constraints exhibiting a nonmonotonic dependence on orbital inclination. These results establish a framework for investigating additional vector-radiation channels in generic EMRIs and their implications for tests of gravity with future space-based gravitational wave observations.

We will re-examine the leading post-Newtonian (1PN) cross terms of hierarchical triples obtained by Lim and Rodriguez (LR) with a two-parameter multiple-scale expansion in the hierarchy parameter $\varepsilon=a_1/a_2$ and the 1PN parameter $\delta$, which disagree with the effective-field-theory result of Kuntz, Serra, and Trincherini (KST) at the orders $\delta\varepsilon^{3/2}$ and $\delta\varepsilon^{7/2}$. Reconstructing the LR calculation, we show that the $\delta\varepsilon^{3/2}$ “libration” term [LR Eq.~(4.5)] originates in the averaging measure: the quadrupole periodic solutions are made mean-free with respect to the outer true anomaly but re-substituted under the time average. The resulting term, evaluated in closed form, reproduces the implemented one exactly; with the time measure required of a canonical generating function it vanishes, in agreement with KST. Equation~(4.5) is one term of the flow of a removable Hamiltonian whose companion terms are absent, which is why it fails the rationality and Hamiltonicity tests. A calculation carried out consistently with a single phase variable yields the complete, gauge-equivalent secular equations, whereas LR's implementation combines a true-anomaly quadrupole solution with an eccentric-anomaly 1PN solution. Two structural defects of the implementation do not contribute to these terms. The $\delta\varepsilon^{7/2}$ term of LR has the correct mass dependence only for $m\ll m_3$, and its angular structure disagrees with KST and violates the Hamiltonicity test. Finally, integrations with LR's secular code show that the resonant ZLK modulations reported by LR survive the removal of Eq.~(4.5), whereas their accelerated merger with the octupole disappears.

This is the second paper of this series in which we prove we can do without dark matter using spacetime with extra dimensions compactified to a hypersphere with radius R. Here we prove cosmological structures can grow even in a Universe without dark matter, provided that extra dimensions are contracting.

Weyl geometry, in which the length scale can be chosen independently at each point of spacetime, provides a natural framework for extending general relativity through Weyl invariance, that is, local scale symmetry. We construct a gravitational theory whose Lagrangian is an arbitrary function of the scalar curvature in Weyl geometry and establish the conditions under which the theory is free of ghosts and tachyons around maximally symmetric vacua. For an arbitrary function, Weyl invariance requires a compensating scalar field in addition to the metric and the Weyl vector. By linearizing the action with an auxiliary field, we show that the Weyl vector couples to the scalar sector only through a single combination of the scalar fields. Consequently, the Weyl vector, shifted by the logarithmic gradient of this combination, becomes a Weyl-invariant massive vector field without gauge fixing. In the Einstein frame, given that the graviton is ghost-free, the no-tachyon condition for the Weyl vector, together with the no-ghost condition for the scalaron, the scalar mode associated with the higher-curvature terms, reduces to the positivity of the kinetic coefficient of the compensating scalar. When this coefficient vanishes, the scalaron does not propagate, leaving only the graviton and the massive vector. As an example, we show that for a Lagrangian containing constant, linear, and quadratic curvature terms, both a massive vector and a massive scalaron are necessarily present throughout the stability region, whereas without the linear term the scalaron becomes massless.

We show that, in Einstein-Cartan theory, the torsion scalar modifies the dust-like equation of state of non-interacting holographic dark energy with the Hubble radius as the infrared cutoff, enabling late-time cosmic acceleration within the low-redshift domain of validity, which is not realized in the corresponding model in general relativity. Using the same holographic dark energy background, we further derive the torsion-induced modification of the cosmic distance duality relation, $d_L=d_A(1+z)^2(1+\eta)$. In the late-time universe, the magnitude of the deviation parameter, $|\eta|$, is small but non-vanishing, reflecting the cumulative effect of torsion along the light-propagation path.

The classification of relativistic closed orbits by their multileaf structures provides a framework for studying strong-field dynamics. Identifying these structures in astronomical images remains challenging. Using ray tracing, we construct the spatiotemporal autocorrelations of the primary image of a pointlike hotspot moving along bound closed geodesics around a Schwarzschild black hole. These orbits are classified by three integers $(z,w,v)$, where $z$ counts the leaves, $w$ counts the additional whirls during each radial period, and $v$ specifies the order in which the orbital leaves are traced. For the orbit families examined, our numerical results establish a correspondence between the topological integers $(z,w,v)$ and the numbers of correlation bands $N_{\rm band}$ and recurrence points $N_{\rm rec}$. The integers are recovered as $z=N_{\rm rec}-1$, $w=\left\lfloor (N_{\rm band}+1)/(N_{\rm rec}-1)\right\rfloor-1$, and $v=(N_{\rm band}+1)\bmod(N_{\rm rec}-1)$. Here, $\lfloor x\rfloor$ denotes the greatest integer not exceeding $x$, and $\bmod$ denotes the remainder operation. These relations provide a quantitative method for recovering closed-orbit topology from hotspot image autocorrelations.

We derive the AdS deformation of the flat-space soft-graviton algebra with Dirichlet boundary conditions. Starting from the AdS$_4$ spinor-helicity representation, we Mellin-transform linearized graviton solutions and construct the AdS wedge, including its Laurent completion. The Dirichlet boundary condition pairs opposite helicities, while AdS covariance fixes their relative normalization. Assuming linear closure and normalizing the global modes to reproduce the geometric AdS isometries, covariance and the Jacobi identities uniquely determine the soft-mode bracket. The result is the wedge of $\mathcal L_\Lambda w_{1+\infty}$, where $\Lambda=-\ell^{-2}$. This provides a bulk derivation of the cosmological-constant deformation that incorporates the AdS boundary condition, without relying on collinear splitting functions or a self-dual truncation.

A black hole growing adiabatically inside a dark matter halo is expected to develop a dense spike, with a power-law slope between 1.5 and 2.5, depending on redshift and baryonic activity. Direct dynamical tests of this prediction are almost non-existent. Here we show that water megamaser disks offer one; their masers orbit within a parsec of the black hole and are mapped individually with very long baseline interferometry, so the enclosed mass at each radius can be read off the rotation curve. We develop a search method and apply it to eleven megamaser disks with public kinematics. Compared with a black hole alone, a spike is preferred in NGC 1194 and NGC 4258 and moderately improves the fit in several others. Allowing the disks to warp removes this preference in all but NGC 4258 and NGC 6264. No combination of disks, warped or not, allows a spike heavier than about ten per cent of the black hole mass, a sensitivity validated with mock injection tests. Mapping the warps with maser accelerations and detecting fainter inner masers, where a spike and a tilt differ most, can break the remaining degeneracy. Megamaser disks open a window onto dark matter around supermassive black holes, and, importantly, one that enables population statistics.

We study how first-order differential observables affect the zero-frequency behavior of black-hole wave equations. Quasinormal modes and late-time tails do not always change in the same way. We give a simple condition for when an observable removes the leading threshold term of a Green function. For Schwarzschild Regge-Wheeler modes, the relevant operator is determined by the regular static solution. The transformation is nondegenerate at nonzero frequency but becomes globally degenerate at zero frequency. As a result, the nonzero quasinormal-mode problem is unchanged, while the leading fixed-radius late-time tail gains one extra inverse power of time.