We investigate the (axial) quasinormal modes of black holes embedded in generic matter profiles. Our results reveal that the axial QNMs experience a redshift when the black hole is surrounded by various matter environments, proportional to the compactness of the matter halo. Our calculations demonstrate that for static black holes embedded in galactic matter distributions, there exists a universal relation between the matter environment and the redshifted vacuum quasinormal modes. In particular, for dilute environments the leading order effect is a redshift $1+U$ of frequencies and damping times, with $U \sim -{\cal C}$ the Newtonian potential of the environment at its center, which scales with its compactness ${\cal C}$.

In relativistic mechanics, the 4-velocity and the 4-momentum need not be parallel. This allows their norm to have a different sign. This possibility occurs in nonlinear electrodynamics (NED) models minimally coupled to Einstein's theory. Surprisingly, for a large class of NED models with a Maxwell limit, for weak fields, the causal (acausal) photons, as determined by their 4-velocity, have a spacelike (timelike) 4-momentum, leading to good tachyons and bad bradyons. Departing from weak fields, this possibility is determined solely by the concavity of the NED Lagrangian, which is consistent with the Dominant Energy Condition analysis. As a corollary, some popular regular black hole solutions sourced by NED, such as the Bardeen and Hayward solutions, are acausal.

We place observational constraints on an FLRW cosmological model in $f(R,L_m)$ gravity with a specific deceleration parameter that depends on the scale factor. This form of the deceleration parameter has been discussed by authors in several papers, but none of them have applied observations to constrain the variables of the model. We carry this out with the cosmic chronometer, supernovae and the baryon acoustic oscillation datasets. The optimum values for the relevant parameters are found and used to plot the kinematical and physical parameters of the model. Although the model tends to the standard Lambda cold dark matter model at late times, there are several issues with the model concerning the values of some of the parameters and the energy conditions. The transition redshift of the model does not match with Planck data. The equation of state parameter indicates that the model falls into the category of phantom dark energy, which is not well supported by observations. Thus, the model does not seem viable.

This paper explores the Friedmann field equations within the framework of Lovelock gravity, a natural extension of Einstein's gravity, focusing on both flat and open universes. Utilizing an approach based on independent Riemann tensor components, we derive generalized Friedmann equations for Lovelock gravity and categorize the solutions into Type I and Type II types. We identify additional vacuum solutions in a flat universe and present a comprehensive solution for a pressure-free scenario in an open universe, both unique to Lovelock gravity. These findings provide new insights into the cosmological implications of Lovelock gravity and offer a foundation for further exploration into the universe's evolutionary trajectory.

We have studied the gravitational wave generated by extreme mass ratio inspirals (EMRIs) along eccentric orbits on equatorial plane within the frame of the swirling-Kerr black hole spacetime. The swirling-Kerr black hole has an extra swirling parameter, which characterizes the rotation of universe background. Our findings indicate that this swirling parameter leads to a delay phase shift in the gravitational waveforms. The impact of the swirling parameter on EMRI gravitational waves is suppressed by the black hole's spin parameter. As a result, extracting information about the swirling parameter from gravitational waves in a static black hole spacetime is much easier than in the case of a rapidly rotating black hole. Our analysis also shows that a high black hole spin leads to a greater overlap of gravitational waveforms for different swirling parameters. We further investigate the potential issue of waveform confusion caused by the orbital eccentricity and semi-latus rectum parameters. As the swirling parameter increases, the relative variation in eccentricity also increases, while the variation in the semi-latus rectum decreases rapidly. The trends in these changes with the swirling parameter resemble those observed with the MOG (Modified Gravity) parameter, though with different rates of change. These results provide deeper insights into the properties of EMRI gravitational waves and the swirling of the universe background.

This paper investigates how rotating traversable wormholes incorporate two cosmic strings at the throat of the wormhole. Building on arXiv:gr-qc/9803098v2 for rotating traversable wormholes and arXiv:gr-qc/0401036 analysis of scalar perturbations, a modified metric that accounts for these cosmic string perturbations is presented. This paper evaluates the Null Energy Condition in the presence of these string perturbations and focuses mainly on the scalar field dynamics in this modified spacetime. Using localized Gaussian perturbations to model cosmic string effects, this paper discusses the impact of angular and radial distributions from the cosmic strings on the spacetime geometry. Regularization has been applied to the shape function and energy condition violations at the wormhole throat, helping to eliminate divergences. The paper concludes with the result that the presence of cosmic strings induces unique anisotropic contributions. Future work could explore gravitational wave signatures associated with similar systems.

We present phenomenological signatures for a modified gravity model f(R), constructed with linear, quadratic, cubic and quartic terms. The obtained signatures satisfy current phenomenological bounds reported by PLANCK and BICEP3. Furthermore, two of the model solutions $\sigma_1$ and $\sigma_2$ seem to favor a much lower value for the tensor-to-scalar ratio $0.0005<r_{\sigma_1}<0.0015$ and $r_{\sigma_2}<0.00015$ than the current reported experimental bounds. The results we obtained are quantitatively similar to those presented in previous studies for $R^3$ models.

The first and second laws of thermodynamics should lead to a consistent scenario for discussing the cosmological constant problem. In the present study, to establish such a thermodynamic scenario, cosmological equations in a flat Friedmann-Lema\^{i}tre-Robertson-Walker universe were derived from the first law, using an arbitrary entropy $S_{H}$ on a cosmological horizon. Then, the cosmological equations were formulated based on a general formulation that includes two extra driving terms, $f_{\Lambda}(t)$ and $h_{\textrm{B}}(t)$, which are usually used for, e.g., time-varying $\Lambda (t)$ cosmology and bulk viscous cosmology, respectively. In addition, thermodynamic constraints on the two terms are examined using the second law of thermodynamics, extending a previous analysis [Phys. Rev. D 99, 043523 (2019) (arXiv:1810.11138)]. It is found that a deviation $S_{\Delta}$ of $S_{H}$ from the Bekenstein-Hawking entropy plays important roles in the two terms. The second law should constrain the upper limits of $f_{\Lambda}(t)$ and $h_{\textrm{B}}(t)$ in our late Universe. The orders of the two terms are likely consistent with the order of the cosmological constant $\Lambda_{\textrm{obs}}$ measured by observations. In particular, when the deviation $S_{\Delta}$ is close to zero, $h_{\textrm{B}}(t)$ and $f_{\Lambda}(t)$ should reduce to zero and a constant value (consistent with the order of $\Lambda_{\textrm{obs}}$), respectively, as if a consistent and viable scenario could be obtained from thermodynamics.

The $3+1$ formalism provides a structured approach to analyzing spacetime by separating it into spatial and temporal components. When applied to the Robertson-Walker metric, it simplifies the analysis of cosmological evolution by dividing the Einstein field equations into constraint and evolution equations. It introduces the lapse function $N$ and the shift vector $N^i$, which control how time and spatial coordinates evolve between hypersurfaces. In standard model cosmology, $N = 1$ and $N^i = 0$ for the Robertson-Walker metric. However, the $N$ becomes a function of time when we apply the metric to the minimally extended varying speed of light model. This approach allows for a more direct examination of the evolution of spatial geometry and offers flexibility in handling scenarios where the lapse function and shift vector vary. In this manuscript, we derive the model's $N$ and $N^i$, along with the constraint and evolution equations, and demonstrate their consistency with the existing Einstein equations. We have shown in a previous paper that the possibility of changes in the speed of light in the Robertson-Walker metric is due to cosmological time dilation. Through the $3+1$ formalism, we can make the physical significance more explicit and demonstrate that it can be interpreted as the lapse function. From this, we show that the minimally extended varying speed of light model is consistent.

Gravitational collapse and bubble evolution in the asymptotical Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe is an intriguing and intricate problem. We systematically analyze dynamics for contact \sch-FLRW (McVittie) spacetimes, focusing on their general junction conditions and introducing a novel function to simplify the extrinsic curvature and surface stress-energy tensor. We explore both static and dynamic scenarios, including special cases such as Schwarzschild, FLRW, and Einstein-Straus configurations by using our general framework. Numerical calculations further reveal the evolution of the concentric McVittie spacetimes with various initial conditions, offering deep insights into the interplay between the McVittie mass parameter and initial peculiar velocity. These results provide a unified perspective for understanding gravitational collapse and bubble evolution in cosmology and astrophysics.

In this work, we focus on the dynamics of a massive one-form field, \textbf{B}, often referred to simply as a vector field, that is minimally coupled to standard Einstein gravity. In the framework of four-dimensional spacetimes, the theory of a massive one-form propagates three massive vector degrees of freedom. The inclusion of a self-interacting potential in this theory results in the breaking of gauge invariance. The breaking of such a fundamental symmetry in Classical Electromagnetism may introduce a ghost mode in massive vector theories, which generally leads to their instability. However, in the context of wormhole physics, the existence of at least one ghost degree of freedom turns out to be a necessary condition to support these exotic geometries within effective field theories. This requirement serves as a strong motivation for our work, wherein we explore the role and phenomenology of massive one-forms, minimally coupled to Einstein gravity, in providing the necessary conditions to sustain wormhole spacetimes. We further analyze the coupling of matter fields to such a vector field through conformal couplings and explore their impact on energy conditions and the physical viability of wormhole solutions.

Recently, a correspondence between quasinormal modes and grey-body factors of black holes has been established. This correspondence is known to be exact in the eikonal regime for a large class of asymptotically flat black holes and approximate when the multipole number \( \ell \) is small. In this work, we demonstrate that there exists a regime where the correspondence holds with unprecedented accuracy even for the lowest multipole numbers: specifically, for perturbations of massive fields in the background of asymptotically de Sitter black holes, provided the field mass is not very small. We also fill the gap in the existing literature via finding the grey-body factors of a massive scalar field in the Schwarzschild- de Sitter background, when $\mu M/m_{P}$ is not small.

We study the transition rates of an atom rotating in a circular orbit, which is coupled with fluctuating electromagnetic fields in vacuum. We find that when the rotational angular velocity exceeds the transition frequency of the atom, the excitation rate can reach the same order of magnitude as the emission rate, even with an extremely low centripetal acceleration resulting from a very small orbital radius. For experimentally accessible centripetal accelerations, the excitation rate of centripetally accelerated atoms can be up to ten to the power of two hundred thousand times that of linearly accelerated atoms with the same acceleration. Our result suggests that the circular version of the Unruh effect can be significant even at very small centripetal accelerations, contrary to the common belief that a large Unruh effect requires large acceleration. This finding sheds new light on the experimental detection of the circular Unruh effect.

Ho\v{r}ava-Lifshitz gravity (to be precise, its projectable version) is recognized as a renormalizable, unitary, and asymptotically free quantum field theory of gravity. Notably, one of its cosmological predictions is that it can produce scale-invariant primordial density fluctuations and primordial gravitational waves without relying on inflation. In this paper, we investigate the quantum nature of the primordial gravitational waves generated in Ho\v{r}ava-Lifshitz gravity. It has been suggested that, for some inflationary models, the non-classicality of primordial gravitational waves in the squeezed coherent quantum state can be detected using the Hanbury Brown - Twiss (HBT) interferometry. We show that in Ho\v{r}ava-Lifshitz gravity, scale-invariant primordial gravitational waves can be generated during both the radiation-dominated and matter-dominated eras of the Universe. Moreover, the frequency range of their quantum signatures is shown to extend beyond that of inflationary models.

We explicitly establish that the Kerr metric represents a pair of self-dual and anti-self-dual gravitational dyons (Taub-NUT instantons). We show that the Newman-Janis algorithm precisely originates from this fact. More generally, this program of understanding four-dimensional black holes as systems of chiral dyons extends to Kerr-Newman and Kerr-Taub-NUT solutions as well.

Modifications of standard general relativity that bring torsion into a game have a long-standing history. However, no convincing arguments exist for or against its presence in physically acceptable gravity models. In this Letter, we provide an argument based on spectral geometry (using methods of pseudo-differential calculus) that suggests that the torsion shall be excluded from the consideration. We demonstrate that there is no well-defined functional extending to the torsion-full case of the spectral formulation of the Einstein tensor.

Multipole moments in general relativity serve as a powerful tool for characterising the gravitational field. In this paper, we review the construction of the Geroch--Hansen multipole moments for stationary asymptotically flat vacuum spacetimes. A particular focus is placed on the well-definedness of these moments, which hinges on the uniqueness of the one-point conformal completion in Geroch's asymptotic flatness definition. Based on Geroch's approach, we formulate and prove a revised uniqueness result, thereby filling in some gaps in the original approach. Uniqueness holds up to certain conformal transformations, and we discuss how the multipole moments behave under such transformations.

The width of a resonance in a nearly integrable system, i.e. in a non-integrable system where chaotic motion is still not prominent, can tell us how a perturbation parameter is driving the system away from integrability. Although the tool that we are presenting here can be used is quite generic and can be used in a variety of systems, our particular interest lies in binary compact object systems known as extreme mass ratio inspirals (EMRIs). In an EMRI a lighter compact object, like a black hole or a neutron star, inspirals into a supermassive black hole due to gravitational radiation reaction. During this inspiral the lighter object crosses resonances, which are still not very well modeled. Measuring the width of resonances in EMRI models allows us to estimate the importance of each perturbation parameter able to drive the system away from resonances and decide whether its impact should be included in EMRI waveform modeling or not. To tackle this issue in our study we show first that recurrence quantifiers of orbits carry imprints of resonant behavior, regardless of the system's dimensionality. As a next step, we apply a long short-term memory machine learning architecture to automate the resonance detection procedure. Our analysis is developed on a simple standard map and gradually we extend it to more complicated systems until finally we employ it in a generic deformed Kerr spacetime known in the literature as the Johannsen-Psaltis spacetime.

We report on work using a newly developed code, SpheriCo.jl, that computes the gravitational collapse of a spherical scalar field, where the scalar can be either a classical field, or a quantum field operator. By utilising summation-by-parts methods for the numerical derivatives we are able to simulate the collapse longer than was possible previously due to enhanced numerical stability. We present a suite of tests for the code that tests its accuracy and stability, both for the classical and quantum fields. We are able to observe critical behavior of gravitational collapse for the classical setup, in agreement with expected results. The code is also used to compute two-point correlation functions, with results that hint at a non-trivial correlation across the horizon of Hawking quanta.

We present a complete method for the initialisation and extraction of first-order inflationary tensor perturbations for fully relativistic simulations which incorporate gravitational back-reaction. We outline a correspondence between the Cosmological Perturbation Theory (CPT) framework and the numerical relativity BSSN variables in the appropriate limit. We describe a generation method for stochastic tensoral initial conditions, inspired by the standard scalar initial condition used from inflation and implemented in lattice cosmology. We discuss the implementation of this procedure in the GRChombo/GRTeclyn code, and demonstrate the detailed quantitative correspondence between the linearised and fully-nonlinear solutions in the perturbative limit, through the evolution of the background and the tensor power spectrum. We also validate the methodology by showing that energy and momentum constraints are introduced and preserved to second-order or better. We provide some preliminary indicative results probing tensoral non-Gaussianity using the skewness and kurtosis. The computational pipeline presented here will be used to study the emergence of a primordial tensor bispectra and cross-spectra that incorporate the effect of nonlinear gravitational couplings with the metric, which has potential applications for the analysis of next-generation CMB surveys.

Recent developments in the consistent embedding of general 4D static and spherically-symmetric spacetimes in arbitrary single-brane braneworld models [Phys.Rev.D 109 (2024) 4, L041501] initiated the program of studying the bulk structure of braneworld wormholes. In this article, adopting a completely generic approach, we derive the general conditions that the metric functions of any braneworld spacetime must satisfy to describe a wormhole structure in the bulk. Particular emphasis is placed on clarifying the proper uplift of 4D wormholes, expressed in terms of various radial coordinates on the brane, and we demonstrate the important role of the circumferential radius metric function for the embedding. Additionally, the flare-out conditions for braneworld wormholes are presented for the first time and are found to differ from the case of flat extra dimensions. To illustrate the method, we first perform the uplift into the Randall-Sundrum II braneworld model for three well-known 4D wormhole spacetimes; the effective braneworld wormhole solutions of Casadio-Fabbri-Mazzacurati and Bronnikov-Kim, and the Simpson-Visser spacetime. Subsequently, we study their bulk features by means of curvature invariants, flare-out conditions, energy conditions and embedding diagrams. Our analysis reveals that the assumption of a warped extra dimension has non-trivial implications for the structure of 5D wormholes.

In the framework of AdS/CFT duality, we consider the semiclassical problem in general quadratic theory of gravity. We construct asymptotically global AdS and hyperbolic~(topological) AdS black hole solutions with non-trivial quantum hair in $4$ and $5$-dimensions by perturbing the maximally symmetric AdS solutions to the holographic semiclassical equations. We find that under certain conditions, our semiclassical solution of hyperbolic AdS black holes can be dynamically unstable against linear perturbations. In this holographic semiclassical context, we also study the thermodynamic instability of the hairy solutions in the $5$-dimensional Gauss-Bonnet theory by computing the free energy and show that depending on the parameter of the Gauss-Bonnet theory, the free energy can be smaller than that of the background maximally symmetric AdS solution in both the global AdS and hyperbolic AdS black hole cases.

We solve the Schr\"odinger-Newton problem of Newtonian gravity coupled to a nonrelativistic scalar particle for solutions with axial symmetry. The gravitational potential is driven by a mass density assumed to be proportional to the probability density of the scalar. Unlike related calculations for condensates of ultralight dark matter or boson stars, no assumption of spherical symmetry is made for the effective gravitational potential. Instead, the potential has only axial symmetry, consistent with the axial symmetry of the particle's probability density for eigenstates of $L_z$. With total angular momentum no longer a good quantum number, there are in general contributions from a range of partial waves. This permits us to study the partial-wave content of self-consistent solutions of the Schr\"odinger-Newton system.

Pulsar timing arrays (PTAs) are essential tools for detecting the stochastic gravitational wave background (SGWB), but their analysis faces significant computational challenges. Traditional methods like Markov-chain Monte Carlo (MCMC) struggle with high-dimensional parameter spaces where noise parameters often dominate, while existing deep learning approaches fail to model the Hellings-Downs (HD) correlation or are validated only on synthetic datasets. We propose a flow-matching-based continuous normalizing flow (CNF) for efficient and accurate PTA parameter estimation. By focusing on the 10 most contributive pulsars from the NANOGrav 15-year dataset, our method achieves posteriors consistent with MCMC, with a Jensen-Shannon divergence below \(10^{-2}\) nat, while reducing sampling time from 50 hours to 4 minutes. Powered by a versatile embedding network and a reweighting loss function, our approach prioritizes the SGWB parameters and scales effectively for future datasets. It enables precise reconstruction of SGWB and opens new avenues for exploring vast observational data and uncovering potential new physics, offering a transformative tool for advancing gravitational wave astronomy.

The detection of a stochastic signal by recent pulsar timing array (PTA) collaborations, including NANOGrav, PPTA, EPTA+InPTA, CPTA and MPTA, has opened a new window to explore gravitational waves (GWs) at nanohertz frequencies. Motivated by the possibility that such a signal could arise from primordial gravitational waves (PGWs), we investigate the implications of tensor non-Gaussianity for the PGW power spectrum. Utilizing PTA data sets, we provide constraints on local-type tensor non-Gaussianity parameter ${F}_{\mathrm{NL}}$. We find $|{F}_{\mathrm{NL}}|\lesssim 7.97$ for a log-normal PGW power spectrum. Our analysis reveals that even moderate tensor non-Gaussianity can lead to significant deviations from standard predictions, thereby offering a novel means to test inflationary scenarios and probe the underlying dynamics of the early Universe. Future multi-band GW observatories, such as LISA, Taiji, and TianQin, will be instrumental in complementing these efforts and further refining our understanding of tensor non-Gaussianity.

Dark matter is believed to account for a significant portion of the mass in the universe, exerting a critical influence on the formation and evolution of cosmic structures. This research delves into the processes of annihilation and decay of dark matter particles, which generate observable signals that deepen our comprehension of their characteristics and behaviors. Furthermore, the study explores the potential role of primordial black holes, with a focus on the emissions of Hawking radiation that could offer valuable insights into their distribution and size range. A key aspect of this investigation revolves around the 21 cm signal, a vital tool for scrutinizing the effects of dark matter particles and primordial black hole phenomena on the intergalactic medium. The upcoming Hongmeng mission, featuring a lunar orbital interferometer array, is poised to revolutionize our ability to observe the 21 cm signal. By conducting measurements devoid of atmospheric disturbances, the mission will significantly boost sensitivity to subtle signals associated with dark matter particle annihilation, decay, and primordial black hole emissions. This study assesses the expected performance of the Hongmeng mission in detecting these telltale signs and aims to unveil fresh insights into the nature and interactions of dark matter particles and primordial black hole emissions through a meticulous analysis of the global 21 cm spectrum. The mission holds immense promise for reshaping our understanding of the universe's concealed components.

Recently proposed $SL(2,\mathbb{Z})$ invariant $\alpha$-attractor models have plateau potentials with respect to the inflaton and axion fields. The slope of the potential in the inflaton direction is exponentially suppressed at large values of the inflaton field, but the slope of the potential in the axion direction is double-exponentially suppressed. Therefore, the axion field remains nearly massless and practically does not change during inflation. The inflationary trajectory in such models is stable with respect to quantum fluctuations of the axion field. We show that isocurvature perturbations do not feed into the curvature perturbations during inflation, and argue that such transfer may remain inefficient at the post-inflationary stage.

We consider the classical field theory whose equations of motion follow from the least action principle, but the class of admissible trajectories is restricted by differential equations. The key element of the proposed construction is the complete gauge symmetry of these additional equations . The unfree variation of the trajectories reduces to the infinitesimal gauge symmetry transformation of the equations restricting the trajectories. We explicitly derive the equations that follow from the requirement that this gauge variation of the action vanishes. The system of equations for conditional extrema is not Lagrangian as such, but it admits an equivalent Hamiltonian formulation with a non-canonical Poisson bracket. The bracket is degenerate, in general. Alternatively, the equations restricting dynamics could be added to the action with Lagrange multipliers with unrestricted variation of the original variables. In this case, we would arrive at the Lagrangian equations for original variables involving Lagrange multipliers and for Lagrange multipliers themselves. In general, these two methods are not equivalent because the multipliers can bring extra degrees of freedom compared to the case of equations derived by unfree variation of the action. We illustrate the general method with two examples. The first example is the particle in central field with varying trajectories restricted by equation of conservation of angular momentum. The phase space gets one more dimension, and there is an extra conserved quantity $K$ which is responsible for precession of trajectories. $K=0$ corresponds to the trajectories of usual Lagrangian dynamics. The second example is the linearized gravity with Einstein-Hilbert action and the class of varying fields is restricted by linearized Nordstr\"om equation. This conditional extrema problem is shown to lead to the linearized Cotton gravity equations.

We study how a charged particle moving in a uniform magnetic field along its standard circular path (cyclotron motion) reacts to a short-duration, homogeneous, uniform electric field pulse injected in the plane perpendicular to the magnetic field. A `permanent' change in the radius of the initial circle and a shift of its centre is noted at later times, after the pulse is switched off. The magnitude of the velocity undergoes a change too, akin to a `velocity kick'. In summary, our results suggest a pulse-induced `electromagnetic memory-like effect', which is not quite a `wave memory', but, nevertheless, has similar features within a simple, non-relativistic context.

In this study, we explore how a non-minimal coupling between dark matter and gravity can affect the behavior of dark matter in galaxy clusters. We have considered the case of a disformal coupling, which leads to a modification of the Poisson equation. Building on an earlier work, we expand the analysis considering all possible disformal coupling scenarios and employing various dark matter density profiles. In doing so, we aim to constrain the key parameter in our model, the characteristic coupling length. To achieve this, we analyze data from a combination of strong and weak lensing using three statistical approaches: a single cluster fitting procedure, a joint analysis, and one with stacked profiles. Our findings show that the coupling length is typically very small, thus being fully consistent with general relativity, although with an upper limit at $1\sigma$ which is of the order of $100$ kpc.

General Relativity famously predicts precession of orbital motions in the Schwarzschild metric. In this paper we show that by adding a NUT charge $N = iM$ the precession vanishes to all orders in $G$ even for rotating black holes. Moreover, we conjecture a generalization of the eikonal formula and show that the classical integrable trajectories determine the full quantum amplitude for this black hole, by means of exponentiation of the Post-Minkowskian radial action. Several consequences of integrability in self-dual gravity are discussed.

We investigate the formation of primordial black holes (PBHs) in an upward step inflationary model, where nonlinearities between curvature perturbations and field fluctuations introduce a cutoff, deviating from the Gaussian case. This necessitates a reevaluation of PBH formation, as $\mathcal{R}$ is not the optimal variable for estimating abundance. Using the extended Press-Schechter formalism, we show that non-Gaussianity modifies both the curvature perturbation profile $\mathcal{R}(r)$ and the integration path in probability space, significantly impacting PBH abundance. Our results reveal that the abundance initially increases with the parameter $h$, which characterizes the relaxation stage after the step. However, beyond a critical value ($h \simeq 5.9$), it sharply declines before rising again. Furthermore, we demonstrate that non-Gaussianity introduces uncertainties in indirect PBH observations via gravitational waves. Notably, we present an example where a positive $f_{\rm NL}$ does not necessarily enhance PBH production, contrary to conventional expectations. Finally, by accounting for non-perturbative effects, we resolve the overproduction of PBHs suggested by pulsar timing array (PTA) data, underscoring the critical importance of incorporating non-Gaussianity in future studies.

We test the standardizability of a homogeneous sample of 41 lower-redshift ($0.00415\leq z \leq 0.474$) active galactic nuclei (AGNs) reverberation-mapped (RM) using the broad H$\alpha$ and H$\beta$ emission lines. We find that these sources can be standardized using four radius$-$luminosity ($R-L$) relations incorporating H$\alpha$ and H$\beta$ time delays and monochromatic and broad H$\alpha$ luminosities. Although the $R-L$ relation parameters are well constrained and independent of the six cosmological models considered, the resulting cosmological constraints are weak. The measured $R-L$ relations exhibit slightly steeper slopes than predicted by a simple photoionization model and steeper than those from previous higher-redshift H$\beta$ analyses based on larger datasets. These differences likely reflect the absence of high-accreting sources in our smaller, lower-redshift sample, which primarily comprises lower-accreting AGNs. The inferred cosmological parameters are consistent within 2$\sigma$ (or better) with those from better-established cosmological probes. This contrasts with our earlier findings using a larger, heterogeneous sample of 118 H$\beta$ AGNs, which yielded cosmological constraints differing by $\gtrsim 2\sigma$ from better-established cosmological probes. Our analysis demonstrates that sample homogeneity$-$specifically, the use of a consistent time-lag determination method$-$is crucial for developing RM AGNs as a cosmological probe.

We perform a detailed study of the gravitational tidal Love numbers of extremal zero-temperature Kerr black holes. These coefficients are finite and exhibit the dissipative nature of these maximally spinning black holes. Upon considering the dynamical behavior of the tidal deformations of the extremal Kerr black holes, we provide explicit expressions of the Love numbers at low frequencies. Their calculation is simplified to specific formulas, which are directly derived using the Leaver-MST methods.

We exploit the results of Bamonti and Gomes (2024) concerning the dynamical (un)coupling of reference frames to gravity to analyse the role of reference frames in the Hole Argument. We introduce a new possible threat to determinism, which we call Arbitrariness Problem (ARB), resulting from the inherent freedom in selecting a reference frame.

We study solutions of the Wheeler DeWitt (WdW) equation in order to recover standard results of cosmological perturbation theory. In mini-superspace, we introduce a dimensionless gravitational coupling $\alpha$ that is typically very small and functions like $\hbar$ in a WKB expansion. We seek solutions of the form $\Psi = e^{iS/\alpha} \psi$ that are the closest quantum analog of a given classical background spacetime. The function $S$ satisfies the Hamilton-Jacobi equation, while $\psi$ obeys a Schr\"odinger-like equation and has a clear probabilistic interpretation. By using the semiclassical limit we express the relation between $\psi$ and the wavefunction of the universe in perturbation theory, $\psi_P$. We apply our formalism to two main examples. The first is a scalar field with a purely exponential potential, of which particularly simple, scaling solutions are known. The other is a slow-roll scenario expanded in the vicinity of the origin in field space. We discuss possible deviations from the classical background trajectory as well as the higher ``time" derivative terms that are present in the WdW equation but not in the perturbative approach. We clarify the conditional probability content of the wavefunctions and how this is related with the standard gauge fixing procedure in perturbation theory.