Papers

We investigate the stability and localization properties of Minkowski, de Sitter (dS), and anti-de Sitter (AdS) thick branes generated by a complex scalar field $\Phi$. The scalar self-interaction potential contains a temperature parameter $a$. As $a$ approaches its critical value, the imaginary part of $\Phi$ becomes double-kinked and the energy density splits into two peaks, indicating the formation of two sub-branes. The analysis of linear scalar, vector, and tensor perturbations shows no signs of instability in the scalar and vector sectors, while the factorization of the tensor perturbation equation excludes tachyonic tensor modes. The graviton zero mode is localized on the Minkowski and dS branes but is not normalizable on the AdS brane. We further study a real test scalar field $\Psi$ with a coupling function $F(R)$ between its kinetic term and the spacetime curvature. The scalar zero mode can always be localized on the Minkowski and dS branes, with a continuous gapless spectrum of scalar Kaluza–Klein (KK) modes. Massive scalar resonances emerge near the critical value of $a$ for suitable values of $\beta$. Increasing $\beta$ produces more resonances and prolongs the lifetimes of the lower resonances, while their time evolution exhibits the characteristic decay of metastable modes. For the AdS brane, the scalar zero mode is also localized, whereas the divergent effective potential at the boundaries traps the massive scalar KK modes as bound states, yielding a discrete mass spectrum.

Entanglement entropy in holographic conformal field theories with boundaries of generic spacetime signature cannot be described entirely within the standard holographic duality to a real bulk spacetime. We show, both in static and time-dependent setups, that an exact match with the conformal field theory predictions in two boundary dimensions entails an extension of the dual spacetime to complex coordinates. As a consequence, relevant bulk objects such as Ryu-Takayanagi surfaces and branes are in general complex, yet anchored on a real asymptotic boundary preserving the physical meaning of field-theoretical quantities. We also provide a third numerical check of the holographic prediction with a two-dimensional system of free Gaussian fermions exhibiting the same asymptotic regimes across different entanglement phases.

It is proved that the affine theory of the full Riemann tensor constitutes the extended theory of gravity. The fundamental object here is a spacetime symmetric connection. Its physical interpretation is that of a field of local inertial frames. In this approach, gravity arises, in a natural way, as a local version of Newton's First Law. A variational formulation of the theory is presented, based on the results introduced in the article co-authored by the present author and one of the supervisors. The general framework is supported by several examples. A central result of the dissertation is the transition from the affine picture to the metric picture. A simplified version of this procedure – valid for a specific class of Lagrangians. It was proved there that the non-metricity in the affine picture can be interpreted as a matter field in the metric picture. This is precisely Hermann Weyl's interpretation of electromagnetism. Here, the transformation from the full Riemann tensor theory to the conventional metric theory is examined in full generality for the first time and illustrated using the previously introduced examples.

We study the granular structure that emerges in a Fuzzy Dark Matter (FDM) halo formed through kinetic relaxation. After the system reaches a virialized core-halo structure, we separate the density field into a smooth spherical component and a residual density that contains the interference pattern characteristic of FDM halos. The power spectrum of this residual field shows a well defined dominant scale, different from the characteristic scale of the total density and of the smooth core-halo model. We compare this granular scale with a local de Broglie wave-lenght calculated from the velocity field obtained from the density current of the system. We find that both scales remain of the same order of magnitude, with the granular scale systematically smaller than the de Broglie wavelength. The radial behavior of the de Broglie wavelength also reveals a non-uniform internal structure, it decreases from the core and reaches its minimum near the transition between the solitonic core and the outer halo. These results provide a quantitative connection between density fluctuations, the local velocity field, and the core-halo morphology of FDM halos.

A novel reinterpretation on the effective one-body (EOB) mapping of compact-body binary (CBB) coalescence was previously considered. Instead of the conventional “marble in a funnel" description of EOB, CBB coalescence is modeled as the concurrent rotation and contraction of a hollow shell with a constant reduced mass measure. Merger is achieved, therefore, when the shell radius reaches the total mass radius. While past works analyzed the energetics sector of the model and the radiated gravitational waves (GWs), this work considers the geometric waveform modeling aspect. More specifically, we mature the mass-shell waveform analysis initially discussed with toy-model conditions by imposing necessary non-conservative mechanics, leading to the analytical expression of usable mass-shell modeled GW-forms. This is to set the foundation for eventual computational endeavors with the analytical waveforms presented here, enabling a comparison against current and state-of-the-art models.

Black holes that merge repeatedly carry a record of that history in their mass distribution. We treat hierarchical merging as a coagulation problem, in which a single kernel encodes how the merger rate depends on the masses involved and on cosmic time, and we derive the late-time spectra that such populations approach. The framework yields closed scaling laws, an exactly solvable benchmark, and a classification of merger environments by a single exponent measuring how strongly mergers favor or suppress massive participants. Applying it to primordial black holes requires care in translating published merger rates into kernel form; done correctly, three of the four standard binary-formation channels map onto superlinear kernels and are therefore candidates for runaway growth, in which the heaviest objects would dominate and no steady mass-conserving spectrum exists; establishing physical gelation, however, requires the full population-dependent kernel and its finite coagulation history, neither of which we settle here. Only the early three-body channel maps into the nongelling regime and admits slow self-similar growth. Numerical solutions across thirteen suppressive, nongelling kernels show that the shape of the spectrum is not fixed by the scaling exponent alone, and that accounting for the energy radiated at each merger measurably changes the high-mass cutoff and drains the population's total black-hole mass.

We show that the logotropic dark fluid, proposed as a single-fluid unification of dark matter and dark energy, is exactly dissipative unimodular gravity with pressureless matter and the logarithmic energy diffusion function $Q(a)=3A\ln a+Q_{c}$. The correspondence is exact at the level of the homogeneous background, rather than asymptotic, and introduces no parameters beyond those already present in either description. It provides a dynamical reinterpretation of the logotropic temperature $A$, whose origin was left open in the original proposal: up to the expansion rate, $A$ is the rate at which energy is diffused from matter into the geometric sector, $\dot Q=3AH$. The adiabatic sound speed of the effective fluid is $c_{s}^{2}=A/\rho$, where $\rho$ is the unimodular matter energy density, and reaches the speed of light at $a_{s}=a_{M}/2^{1/3}$; the matter energy density then vanishes and changes sign at $a_{M}$, which is precisely the scale factor at which the model is known to become phantom. Since $\rho$ coincides with the enthalpy density $\epsilon+P$ of the logotropic fluid, the phantom branch is the branch on which the matter sector carries negative energy density and on which the apparent horizon entropy decreases. Finally, we show that a one-parameter saturating diffusion law removes these late-time pathologies while preserving the low-redshift phenomenology.

We use a point-particle effective field theory to study the superradiant instability rates of an ultralight massive vector around a slowly rotating black hole. Earlier effective-theory treatments reported an apparent $O(1)$ discrepancy with the rates obtained by solving the Proca equation on a fixed black-hole background, e.g. for the mode with $j=1$ and $\ell=2$. We show that there is in fact no discrepancy: once the leading-order states in the degenerate $\{\ell=0,\ell=2\}$ subspace are correctly identified, the effective theory (implemented here with the graviton integrated out exactly, and expanded in $\alpha$ only afterwards) reproduces all of the $j=1$ Proca instability rates exactly, and it does so without ever invoking the FKKS ansatz on which the full-theory calculation rests. Since it never relies on separability, the same approach applies, at least in principle, to rotating backgrounds and bodies that lack the hidden symmetries underlying that ansatz. The single ingredient beyond the far zone is a conservative worldline contact term, the static monopole response of the horizon in the parity-even $j=1$ Proca sector, which we fix by matching to the near zone. The same term shifts the fine-structure splitting of the bound states into exact agreement with the published Proca spectrum. In addition to providing a conceptually straightforward model of vector superradiance and resolving an apparent tension in the literature, we present this work to illustrate potential technical subtleties involving dissipative effects in point particle effective theories.

We study a zero temperature, degenerate, fermion gas with fermions of rest mass $m$, that only interacts with itself, gravitationally. We describe a self-consistent novel approach to the formation of a degenerate, quantum mechanical, star. In this approach, the fermions occupy the energy levels that are determined by the self consistent gravitational interactions, according to the Pauli exclusion principle. Then the size of the highest occupied level determines the radius of the star. In the Newtonian gravitational limit, the fermions feel a potential corresponding to a simple harmonic well that smoothly attaches in the exterior to the usual $1/r$ Newtonian gravitational potential. We find analytically, solutions for stars with any radius and mass, parametrized by $m$ and $N_s$, the total number of fermions. In the Newtonian limit, we easily find that we can construct a star that is more compact than the Buchdahl bound and indeed can even be smaller than the Schwarzschild radius. Clearly, such cases are outside of the purview of the Newtonian limit. Therefore we expand our analysis to fermions in the general relativistic context, interacting gravitationally with a metric. We consider the metric corresponding to the interior Schwarzschild solution smoothly connecting to the usual exterior Schwarzschild metric. Treating matter semi-classically, we recover the Buchdahl bound in a completely independent analysis. We briefly discuss classical stability of the Newtonian solution, and its relation to Newtonian polytropic fluids.

Gravitational waves couple in a nonlinear fashion in the vicinity of a black hole. Black hole perturbation theory can be readily applied to compute the magnitude of this coupling, its dependence on the parity content, frequencies, and angular structure of the incoming gravitational waves. In this work we carry out this calculation, showing how the nonlinear coupling of gravitational waves generically peaks when the driven frequency matches the oscillation frequency of the fundamental quasinormal mode of the black hole. We also demonstrate how this excitation is largest at the maximal harmonics allowed, and study its dependence on the parity content of the incoming modes. At low frequencies, the quadratic response computed here encodes the nonlinear, dynamical tidal deformability of the black hole spacetime itself. We demonstrate numerically that the quadratic black hole coupling coefficient scales quadratically with the driving frequency, and recover this scaling from the 5-point Compton graviton scattering amplitude.

Thermodynamic topology provides a topological classification of black hole states and their branch structures in thermodynamic parameter space. We investigate the thermodynamic topology of the charged nonextremal magnetic Gibbons–Maeda family in four-dimensional asymptotically flat Einstein–Maxwell–dilaton gravity, with particular emphasis on its string-theory member at the dilaton coupling $a=1$, the Gibbons–Maeda–Garfinkle–Horowitz–Strominger (GMGHS) black hole. An analytic classification over the complete domain of regular outer horizons shows that the dilaton coupling separates the family into three limiting structures of the inverse Hawking temperature. At $a=1$, the GMGHS defect curve approaches a nonzero lower inverse temperature endpoint and contains a single unstable branch. In particular, the magnetic GMGHS black hole provides an explicit realization of the previously proposed $\overline W^{1-}$ thermodynamic topological subclass within an asymptotically flat Einstein–Maxwell–dilaton solution. This result demonstrates that the global topological number $W$ alone does not completely characterize black hole thermodynamic topology. The asymptotic behavior of the inverse Hawking temperature near the boundaries of the physical horizon domain provides an additional criterion for distinguishing thermodynamic topological subclasses with the same $W$.

Among all gravitational solutions, traversable wormholes stand out as truly fascinating, yet within general relativity, they almost always demand exotic matter that necessarily violate null energy requirement. The inclusion of matter-geometry coupling in modified gravity theories provides a viable platform where wormholes remain open which are supported by effective gravitational field. We therefore examine the structure and properties of slowly rotating traversable wormholes using the $f(R,T)$ framework. We formulate stationary wormhole models coupled with the anisotropic fluid and show that they are regular, horizon-free, approach a flat spacetime geometry at large distances, and satisfy the flare-out requirement at the throat. Our results indicate that the required matter meets both the null and strong energy conditions, demonstrating that rotating wormholes do not necessarily require unconventional sources. We further study particle trajectories, frame dragging phenomena, and non-geodesic behavior resulting from matter-geometry coupling, alongside the weak-field and lensing effects caused by the rotation. Our results establish the potential astrophysical viability of rotating wormholes in $f(R,T)$ gravity.

We prove linear stability of Kasner spacetimes in the direction of the Big Bang, up to an explicit finite dimensional space of non-decaying self-similar solutions. The fastest growing solution is the linearization of Taub's explicit Bianchi II solution, describing a Kasner transition. All other non-decaying solutions are inhomogeneous analogues of this, and the linearized Kasner metric. The key novelty is a notion of quasinormal modes on Kasner spacetimes, similar to quasinormal modes on stationary black holes spacetimes. All quiescent (as opposed to oscillatory) vacuum Big Bang spacetimes of dimension 4 are asymptotic to a Kasner spacetime from the perspective of a single observer at the Big Bang. They are expected to be highly unstable due to the oscillations conjectured by Belinski, Khalatnikov and Lifschitz. This paper provides a complete description of this instability on a linear level without symmetry assumptions.

Quantum effects are expected to modify a black hole's interior structure, particularly near the singularity. We show how to extract the scaling exponent of the singularity from the quasinormal mode (QNM) spectrum of a massless scalar probe in the asymptotic large-overtone limit. We apply our method to a family of exact quantum black holes in (2+1)-dimensional anti-de Sitter (AdS) space and explicitly uncover a transition deep in the interior when quantum effects become dominant.

We develop a hydrodynamic effective field theory for the gravitational dynamics of compact objects moving through an inviscid fluid environment. The fluid is described by the effective theory of perfect fluids, whose Goldstone phonons are kept as explicit fields coupled to gravity. We establish a consistent power counting for the resulting Feynman rules and derive the propagators and interaction vertices through four points in $D$ dimensions, together with the generalized on-shell Ward identities they obey. These identities relate amplitudes with an external graviton to those with the graviton replaced by a phonon, and thus provide nontrivial checks on higher-order calculations. As an application, we recover the leading-order relativistic dynamical-friction force from the tree-level amplitude for single-phonon emission. This work is a first step towards a toolkit for incorporating environmental effects into the scattering-amplitude pipeline used in post-Minkowskian calculations.

In this work, we implement at the quantum level the gauge-fixing conditions that relate the homogeneous SU(2) gauge theory of Ashtekar variables, describing the classical cosmological sector, to the usual minisuperspace formulation. We impose the so-called divergence constraint, which fixes the gauge to the homogeneous one and, at the classical level, recovers a finite-dimensional phase space, together with the diagonal constraint, which imposes the diagonality of the metric and has already been extensively studied in the literature. We construct the corresponding quantum operators for general cosmological models and provide a suitable regularization in terms of holonomies and fluxes. We then show that a special class of homogeneous spin-network states describing the Bianchi I and Bianchi IX models satisfies the quantum gauge-fixing constraints, using techniques developed in Reduced Quantum Loop Gravity. This provides a quantum-level link between the cosmological theory with full SU(2) gauge symmetry and standard Loop Quantum Cosmology, by reason of the effective Abelian structure of the selected states.

We present a real time formalism to numerically describe the gravitational collapse of a scalar quantum field in the spherically symmetric case. We employ a Pauli-Villars regulator that is specifically designed to cancel the ultraviolet divergences in the energy-momentum tensor identified by covariant point splitting, including the logarithmic ones. Using this regulator, we find that the leading term of the entanglement entropy, which is proportional to the surface area, vanishes for a spherical region of flat spacetime. First numerical results for the dynamical case indicate that for a collapsing shell of a massless scalar field, the area normalized entropy is concentrated on the shell and has an approximately constant maximum value during time evolution. This maximum value appears to be finite in the continuum limit and only mildly dependent on the regulator mass.

We introduce new coordinates that extend the Kerr–Newman–Bertotti–Robinson spacetime consistently with the previous reciprocal continuation. In these coordinates, the two points at $\Omega=0$ are resolved into complete Bertotti–Robinson null infinities. The extended spacetime describes two black holes sharing a common exterior of nontrivial topology, together with a naked ring singularity. In the regular static limit, the new coordinates globally identify the spacetime with the balanced Alekseev–García geometry.

We study single-field slow-roll inflation in the context of Palatini gravity for the class of non-minimally coupled $\xi$-attractors, i.e.,\ models where the same function $f(\phi)$ fixes both the non-minimal coupling, $1+\xi f(\phi)$, and the inflationary potential, $V(\phi) = M^4 f(\phi)^2$. For an arbitrary $f(\phi)$, the number of $e$-folds is, at leading order, independent of $\xi$. Thanks to this, we provide an immediate mapping between the observables of the non-minimally coupled setup and those of the minimally coupled one. In the strong coupling limit, the tensor-to-scalar ratio is, as usual, suppressed, while the scalar spectral index is shifted towards larger values, with the magnitude of the shift depending only on the tensor-to-scalar ratio associated with the original potential $V(\phi)$.

In this paper we propose a geometrically motivated formulation of gravity in an invariant Weyl–Integrable space-time (IWIST), in which the background geometry is not imposed a priori but is dynamically determined through the Palatini variational principle. For a scalar field non-minimally coupled to gravity action, the resulting compatibility condition defines a Weyl–Integrable geometry which is preserved by a local Weyl transformation of the metric and the geo\-me\-tri\-cal scalar field. We construct an action invariant under both diffeomorphisms and Weyl transformations and introduce a Weyl-covariant variational procedure based on an invariant extension of the divergence theorem. The corresponding field equations are obtained for the metric, the Weyl scalar, and the Weyl gauge field. We further formulate the theory in the Einstein–Riemann frame, where the effective metric is Riemannian and the scalar field is re\-inter\-pre\-ted as a phy\-si\-cal degree of freedom of geometric origin. Finally, we propose a geometrical mechanism for the explicit breaking of Weyl symmetry by introducing a coupling between the Weyl gauge field and a current constructed from the scalar sector. The resulting theory remains diffeomorphism covariant while departing from local Weyl invariance. The Einstein–Riemann representation of the broken theory contains an additional generally covariant interaction, making the Weyl-invariant model a particular limit of a more general gravitational theory.

We review Raju's all-line recursion relations for Yang-Mills theory in AdS${}_4$ and evaluate four-point correlators for the All-plus, Single-minus, and MHV helicity configurations. We point out the relevant deformation for the legs needed to obtain the correlators. In particular, we explicitly derive the expressions for all the residues contributing to all three correlators. We also perform an explicit numerical check with the results computed by Witten diagram computations and find perfect agreement with our results. Finally, we conclude by discussing some applications of these recursions for obtaining higher-point functions.

We investigate the scalar quasinormal mode (QNM) spectrum of Schwarzschild-AdS black holes with a partially reflective surface placed near the event horizon. The corresponding QNM problem is solved numerically using Chebyshev spectral collocation. The resulting spectra exhibit a characteristic cavity structure at sufficiently large real part, where the modes form approximately equally spaced sequences whose spacing and damping are controlled mainly by the cavity length and the surface reflectivity. For large AdS radius, an additional weakly damped quasibound-state branch appears due to trapping between the centrifugal barrier and the AdS potential wall. We show that these spectral features can be understood within a finite radial cavity picture. A WKB analysis provides a quantitative asymptotic description of the spectra which have high real parts. We find that changes in the near-horizon boundary condition can lead to substantial changes in the QNM spectrum, indicating the strong sensitivity of Schwarzschild–AdS QNMs to the effect of horizon correction.

We study spontaneous scalarization near and at extremality in Einstein-Maxwell-scalar theory. As Reissner-Nordström (RN) extremality is approached from below, the nonextremal scalarization existence curves collapse toward a common critical threshold $\alpha_c=1/4$ given by the Breitenlohner-Freedman bound for the near-horizon throat (AdS$_2\times S^2$) of its extremal black hole. For a polynomial coupling, we construct extremal black holes with nonconstant scalar hair, satisfying $M^2+Q_s^2=Q^2$, which places them in the overcharged region $Q/M>1$ beyond the RN bound. A common near-region phase mechanism predicts accumulation toward the RN extremality from both sides, yielding Miransky-type scaling. In the extremal sector, the logarithmic phase interval doubles, halving the exponent which denotes the geometric spacing of successive node scales.

Gravitational-wave observations of binary neutron star mergers probe the neutron star equation of state through finite-size effects on the waveform. These include the tidal deformation of the stars due to their respective companion, but for spinning neutron stars also include the spin-induced quadrupole moment of the stars. Typically, to avoid introducing additional equation of state dependent parameters, waveform models relate this quadrupole moment to the tidal deformability through so-called quasi-universal relations. These are derived under the slow-rotation approximation, which at larger spins, i.e., for millisecond pulsars, becomes unreliable. We attempt to extend the existing quasi-universal relations by explicitly accounting for the spin, calibrating it against numerically computed quadrupole moments across a broad set of equations of state and spins $0.15 \leq |\chi| \leq 0.6$ with the $\chi\rightarrow 0$ limit enforced by construction. The resulting spin-extended relation reduces the median absolute percentage error relative to the slow-rotation relation by 66% across this range. Parameter estimation using the spin-extended relation reduces biases in recovered intrinsic parameters in some cases, though biases from mass-spin degeneracies dominate largely when a population is considered. These results provide a more accurate description of the spin-induced quadrupole moment for spinning neutron star binaries, relevant for waveform modelling with third-generation gravitational-wave detectors.

We prove a positive mass theorem for one-ended asymptotically flat spin initial data with multiple time directions and a smooth compact boundary. Assuming the trace-norm dominant energy condition and pairwise commutativity of the second fundamental forms, a fixed auxiliary time direction on each boundary component determines a local chirality condition. We identify the surviving mixed boundary term and obtain the inequality $E\geq\|\mathcal P\|_{\mathrm{tr}}$ under the boundary condition $H+\operatorname{tr}_\Sigma k^T+\|\mathcal Q_T\|_{\mathrm{tr}}\leq0$. The proof constructs a Dirac–Witten harmonic spinor in an affine energy space and evaluates the mass identity by approximation. We also establish the pointwise sharpness of this boundary condition for the fixed projector and give two-time data with a nonzero mixed boundary term.

Recent measurements of cosmic expansion have renewed interest in dark-energy scenarios in which the effective equation of state exhibits phantom-like evolution and may cross $w=-1$. Such behavior, however, does not require a fundamental phantom field: in coupled dark-energy-dark-matter~(CDEDM) models, energy exchange between a canonical scalar field and cold dark matter, happens Lagrangian labels, can reproduce the same effective equation of state evolution as that of phenomenological $w_0w_a$CDM model. We show that this microscopic interaction leaves distinctive, testable signatures in structure growth by forming a two-fluid system in which only cold dark matter feels the scalar-mediated fifth force (and an associated drag term), while baryons remain uncoupled. When combined with neutrino-free streaming, this setup generates a characteristic coupling, neutrino-mass degeneracy, whose leading scaling $\sum m_\nu \propto f_c^2 \alpha^2$ follows analytically from the two-fluid growth equations. Using DESI DR2 BAO, CMB distance information, ACT DR6 lensing, redshift-space distortions, and three supernova compilations, we find that this scaling is recovered for both exponential and inverse-power-law potentials. We further show that the dominant contribution to the growth response arises from the coupling-induced modification of the background evolution, with the fifth force enhancing growth and the drag partially counteracting it. Finally, the interaction induces a running dark-matter mass, changing it at recombination by $4.3\%$–$5.5\%$, so CMB distance calculations must account for the evolving dark-matter density. These correlated growth and recombination effects provide a route to distinguish interaction-driven phantom crossing from purely kinematic dark-energy parametrizations.

We investigate matter creation in the cosmological framework of unimodular gravity. We keep the energy density $\rho$, pressure $p$, particle number density $n$, and particle number $N=nV$ as the physical thermodynamic variables of the matter sector, and introduce particle creation directly through the balance equation $N^{\mu}{}_{;\mu}=n\Gamma$. Combining this open-system formulation with the unimodular diffusion term $Q$, we derive the exact identity $nT\dot\sigma=-3Hp_c-(\rho+p)\Gamma-\dot Q$, which shows that the creation pressure $p_c$, the creation rate $\Gamma$, and the diffusion term $Q$ are, in general, three independent sources of entropy production per particle. Adopting the standard postulate that particle creation is itself adiabatic, the first two terms cancel identically and the relation reduces to the particular case $nT\dot\sigma=-\dot Q$, so that the entropy per particle is constant only when $Q$ is constant. Thus, even when the creation process associated with $\Gamma$ is adiabatic in the usual Prigogine sense, the full matter evolution in unimodular gravity is non-adiabatic whenever $\dot Q\neq0$. The general identity, however, remains available as a starting point for relaxing this postulate in future work.

Ultra-light dark matter, composed of bosons behaving as classical waves, can resonantly excite stellar oscillations. In this work, we investigate this phenomenon in relativistic stars, showing that $\ell=0$ fluid modes can be excited. We derive a framework for calculating the mode amplitude and apply it to neutron stars to predict the associated surface temperature fluctuations; the resulting signal lies beyond current observational sensitivities. We discuss prospects for extending this approach to other compact objects.

In single-field inflation, linear perturbations originate as quantum fluctuations and undergo a quantum-to-classical transition on super-horizon scales as the decaying mode of the comoving curvature perturbation $\mathcal{R}$ is suppressed. This transition provides a condition for the validity of a classical stochastic description of $\mathcal{R}$. We characterize classicality through the suppression of the quantum commutator relative to phase-space variances and the evolution of the squeezing parameters. In the Starobinsky model, we show that this transition becomes mode-dependent at linear order due to the transient ultra-slow-roll (USR) phase. This is because the decaying mode transiently grows during the USR phase modifying the squeezing dynamics, and shifting the classicalization time depending on when modes exit the horizon relative to the USR phase. We then study the implications of this mode-dependent transition for the stochastic description of perturbations. Using the Green's function method, we show that the stochastic spectrum reproduces the power spectrum of the quantum state initialized in the Bunch-Davies vacuum, independently of the mode-dependent transition when the gradient term is retained in the Langevin equation, for both white and colored noise coarse-graining. In contrast, ignoring the gradient term in the Langevin equation introduces an explicit dependence on the coarse-graining parameter $\sigma$. Homogeneous matching procedure can be used to set mode-dependent $\sigma(k)$ that reproduces the power spectrum of the quantum state at the end of inflation. Crucially, however, we show that the matching times precede the classicalization times for modes near the USR transition. Therefore, the transient USR phase in this model leads to a mode-dependent condition for when linear curvature perturbations can be described as classical stochastic noise.

Gravitational-wave (GW) memory is a permanent change in spacetime geometry induced by a burst of gravitational waves. It is theoretically interesting for its connection to asymptotic symmetries, but has not yet been observed. The upcoming Laser Interferometer Space Antenna (LISA) is predicted to detect memory directly in loud events from supermassive black hole (SMBH) mergers. We assess the prospects for the cumulative effect of memory contributions as a stochastic GW memory background (SGWMB). Using two SMBH population models, we recover previously obtained single-event SNR forecasts and compute the power spectrum of the unresolved background, using numerical-relativity waveforms for modeling the memory signal during each event. We find the predicted spectrum is significantly smaller than ones found by modeling the memory waveform with a Heaviside function, with expected SNRs of order $O(0.1-10)$. We further find that our models favor a highly non-Gaussian ("popcorn") spectrum, demonstrating that the background may not appear as the union of continuous, overlapping signals, but rather as a collection of intermittent bursts. In both measures, we demonstrate that any current prediction of the spectrum is heavily dependent on the choice of population model. We interpret these findings in the light of the future LISA mission and emphasize their importance for properly handling memory within the LISA global fit.