We show that the Raychaudhuri equation remains invariant for certain solutions of scalar fields $\phi$ whose Lagrangian is non-canonical and of the form $\mathcal{L}(X,\phi)=-V(\phi)F(X)$, with $X=\frac{1}{2} g_{\mu\nu} \nabla^{\mu}\phi \nabla^{\nu} \phi$, $V(\phi)$ the potential. Solutions exist for both homogeneous and inhomogeneous fields and are reminiscent of inflaton scenarios.

This paper presents the first numerical study of black hole thermodynamics in Causal Set Theory, focusing on the entropy of a Schwarzschild black hole as embodied in the distribution of proposed horizon molecules. To simulate causal sets we created a highly parallelized computational framework in \texttt{C++} which allowed for the generation of causal sets with over a million points, the largest causal sets in a non-conformally flat spacetime to date. Our results confirm that the horizon molecules model is consistent with the Bekenstein-Hawking formula up to a dimensionless constant that can be interpreted as the fundamental discreteness scale in the order of a Planck length. Furthermore, the molecules are found to straddle the horizon of the black hole to within a few Planck lengths, indicating that entropy lives on the surface of the black hole. Finally, possible implications for the information paradox are drawn. In particular, we show how the horizon molecules model could yield a finite black hole temperature cut-off or even prevent full black hole evaporation.

The Polynomial Affine Gravity is an alternative gravitational model, where the interactions are mediated solely by the affine connection, instead of the metric tensor. In this paper, we explore the space of solutions to the field equations when the torsion fields are turned on, in a homogeneous and isotropic (cosmological) scenario. We explore various metric structures that emerge in the space of solutions.

We currently lack good waveform models for many gravitational wave sources. Examples where models are lacking include neutron star post merger signals, core collapse supernovae, and signals of unknown origin. Wavelet based techniques have proven effective at detecting and characterizing these signals. Here we introduce a new method that uses collections of evolving amplitude-frequency tracks, or "voices", to model generic gravitational wave signals. The analysis is implemented using trans-dimensional Bayesian inference, building on the earlier wavelet-based BayesWave algorithm. The new algorithm, BayesWaveVoices, outperforms the original for long duration signals.

In this article, we apply the Finsler spacetime to develop the Einstein field equations in the extension of modified geometry. Following Finsler geometry, which is focused on the tangent bundle with a scalar function, a scalar equation should be the field equation that defines this structure. This spacetime maintains the required causality properties on the generalized Lorentzian metric manifold. The matter field is coupled with the Finsler geometry to produce the complete action. In this work, we use modified gravity to develop the Einstein field equations from the variational principle. Developed Einstein field equations are employed on the strange stellar system to improve the study. The interior of the system is made of a strange quark, maintained by the MIT Bag equation of state. In addition, the modified Tolman-Oppenheimer-Volkov (TOV) equation is formulated. In particular, the anisotropic stress attains the maximum at the surface. The mass-central density variation justifies the stability of the system.

A semiclassical investigation of the electromagnetic radiation emitted by a charged particle in a radially freely falling motion in Schwarzschild spacetime is carried out. We use quantum field theory at tree level to obtain the one-particle-emission amplitudes. We analyze and compare the energy spectrum and total energy released, which are calculated from these amplitudes, for particles with varying initial positions and for particles originating from infinity with varying kinetic energy. We also compare the results with those due to a falling charged "string" extended in the radial direction.

Higher-order theories of gravity are a branch of modified gravity wherein the geometrodynamics of the four-dimensional Riemannian manifold is determined by field equations involving derivatives of the metric tensor of order higher than two. This paper considers a general action built with the Einstein-Hilbert term plus additional curvature-based invariants, viz. the Starobinsky $R^{2}$-type term, a term scaling with $R^{3}$, and a correction of the type $R\square R$. The focus is on the background inflationary regime accommodated by these three models. For that, the higher-order field equations are built and specified for the FLRW line element. The dynanical analysis in the phase space is carried in each case. This analysis shows that the Starobinsky-plus-$R^{3}$ model keeps the good features exhibited by the pure Starobinsky inflationary model, although the set of initial conditions for the inflaton field $\chi$ leading to a graceful exit scenario is more contrived; the coupling constant $\alpha_{0}$ of the $R^{3}$ invariant is also constrained by the dynamical analysis. The Starobinsky-plus-$R\square R$ model turns out being a double-field inflation model; it consistently enables an almost-exponential primordial acceleration followed by a radiation dominated universe if its coupling $\beta_{0}$ takes values in the interval $0\leq\beta_{0}\leq3/4$. The models introducing higher-order correction to Starobinsky inflation are interesting due to the possibility of a running spectral index $n_{s}$, something that is allowed by current CMB observations.

The $U(1)$ gauge-invariant scalar-vector-tensor theories, which catches five degrees of freedom, are valuable for its implications to inflation problems, generation of primordial magnetic fields, new black hole (BH) and neutron star solutions, etc. In this paper, we derive conditions for the absence of ghosts and Laplacian instabilities of nontrivial BH solutions dressed with scalar hair against both odd- and even-parity perturbations on top of the static and spherically symmetric background in the most general $U(1)$ gauge-invariant scalar-vector-tensor theories with second-order equations of motion. In addition to some general discussions, several typical concrete models are investigated. Specially, we show that the stability against even-parity perturbations is ensured outside the event horizon under certain constraints to these models. This is a crucial step to check the self-consistency of the theories and to shed light on the physically accessible models of such theories for future studies.

This paper combines the post-Minkowskian expansion of general relativity with the language of intersection theory. Due to the nature of the soft limit inherent to the post-Minkowskian expansion, the intersection-based approach is of enhanced utility in that theory compared to a generic QFT. In the language of intersection theory, Feynman integrals are rephrased in terms of twisted cocycles. The intersection number is a pairing between two such cocycles and its existence allows for the direct projection onto a basis of master integrals. In this paper we use this approach to compute the 2PM contribution to the scattering of two compact astronomical objects, getting results in agreement with previous findings.

Gravitational-wave memory is a non-linear effect predicted by general relativity that remains undetected. We apply a Bayesian analysis framework to search for gravitational-wave memory using binary black hole mergers in LIGO-Virgo-KAGRA's third gravitational-wave transient catalogue. We obtain a Bayes factor of $\ln \text{BF}=0.01$, in favour of the no-memory hypothesis, which implies that we are unable to measure memory with currently available data. This is consistent with previous work, suggesting that a catalogue of $\mathcal{O}(2000)$ binary black hole mergers is needed to detect memory. We look for new physics by allowing the memory amplitude to deviate from the prediction of general relativity by a multiplicative factor $A$. We obtain an upper limit of $A<23$ ($95\%$ credibility).

We investigate the entanglement generation or harvesting between two identical Unruh-DeWitt detectors in the cosmological de Sitter spacetime. We consider two comoving two-level detectors at a coincident spatial position. The detectors are assumed to be unentangled initially. The detectors are individually coupled to a scalar field, which eventually leads to coupling between the two detectors. We consider two kinds of scalar fields -- conformally symmetric and massless minimally coupled, for both real and complex cases. By tracing out the degrees of freedom corresponding to the scalar field, we construct the reduced density matrix for the two detectors, whose eigenvalues characterise transitions between the energy levels of the detectors. By using the existing results for the detector response functions per unit proper time for these fields, we next compute the logarithmic negativity, quantifying the degree of entanglement generated at late times between the two detectors. The similarities and differences of these results for different kind of scalar fields have been discussed.

In this paper, we extend Chandrasekhar's method of calculating rotating black holes into $f(R)$ theory. We consider the Ricci scalar is a constant and derive the Kerr and Kerr-Ads metric by using the analytical mathematical method. Suppose that the spacetime is a 4-dimensional Riemannian manifold with a general stationary axisymmetric metric, we calculate Cartan's equation of structure and derive the Einstein tensor. In order to reduce the solving difficulty, we fix the gauge freedom to transform the metric into a more symmetric form. We solve the field equations in the two cases of the Ricci scalar $R=0$ and $R\neq 0$. In the case of $R=0$, the Ernst's equations are derived. We give the elementary solution of Ernst's equations and show the way to obtain more solutions including Kerr metric. In the case of $R\neq 0$, we reasonably assume that the solution to the equations consists of two parts: the first is Kerr part and the second is introduced by the Ricci scalar. Giving solution to the second part and combining the two parts, we obtain the Kerr-Ads metric. The calculations are carried out in a general $f(R)$ theory, indicating the Kerr and Kerr-Ads black holes exist widely in general $f(R)$ models. Furthermore, the whole solving process can be treated as a standard calculation procedure to obtain rotating black holes, which can be applied to other modified gravities.

The present work investigates the general wormhole solution in Einstein gravity with an exponential shape function around an ultrastatic and a finite redshift geometry. The geodesic motion around the wormholes is studied in which the deflection angle of the orbiting photon sphere is found to be negative after a certain region, indicating the presence of repulsive effect of gravity in both the ultrastatic and finite redshift wormholes. Various unbounded and bounded timelike trajectories are presented on the wormhole embedding diagrams, in which some of the bound orbits involve intersection points that may lead to causality violating geodesics. Another class of closed timelike geodesics are obtained in the unstable circular trajectory that appeared at the wormhole throat. Finally, the trajectories are classified in terms of the family of CTG orbits.

A yet undetected class of GW signals is represented by the close encounters between compact objects in highly-eccentric e~1 orbits, that can occur in binary systems formed in dense environments such as globular clusters. The expected gravitational signals are short-duration pulses that would repeat over a much longer time scale in case of multiple passages at periastron. These sources represent a unique opportunity of exploring astrophysical formation channels as well as a different way of testing GR. In the case of binary systems containing neutron stars, the observation of these sources could help to constrain the EOS, thanks to the signature left in the GW signal by the f-modes excitation that can occur during the encounter. The detection and PE of these signals is challenging given the short duration of expected signals and the sensitivities of current ground-based GW interferometers. We present a novel approach that exploits Probabilistic ML. We have used Conditional Normalizing Flows to model complex probability distributions and therefore infer posterior distributions for the source parameters. Fast detection and PE is very important as it could trigger electromagnetic follow-up campaigns and offer the possibility to study these events in a multimessenger context. To develop and test the algorithm, we have focused on the simulations of single bursts emission obtained using the Effective Fly-by formalism and embedded in the noise of aLIGO and Virgo during O3. Our proposed model outperforms standard Bayesian methods in accuracy and is 5 orders of magnitude faster, being able to produce 5x10^4 posterior samples in just 0.5s. The results are extremely promising and constitute the first successful attempt for a fast and complete parameter estimation of binary CEs using deep learning, offering a new approach to study the evolution of orbital parameters of compact binary systems.

The gravitational-wave signal GW170817 is a result of a binary neutron star coalescence event. The observations of electromagnetic counterparts suggest that the event didn't led to the prompt formation of a black-hole. In this work, we first classify the GW170817 LIGO-Virgo data sample into prompt collapse to a black-hole using the $q$-dependent threshold mass fits and then remove these cases from the data sample. We find that the cases without a prompt black-hole formation do not support radii $ <$ 10 km unlike the LIGO-Virgo data sample. This is consistent with the maximum mass constraint, based on the binary pulsar J0348+0432, imposed LIGO-Virgo data sample. Additionally, we find that the cases without the prompt collapse to a black-hole improve the uncertainty range of neutron star radii from 3.3 km to 2.6 km for the data sample without the mass constraint and from 2.8 km to 2.5 km for the data sample with the mass constraint, implying improved constraints on the neutron star radii and hence the equation-of-state.

This paper investigates Buchdahl transformations within the framework of Einstein and Einstein-Scalar theories. Specifically, we establish that the recently proposed Schwarzschild-Levi-Civita spacetime can be obtained by means of a Buchdahl transformation of the Schwarschild metric along the spacelike Killing vector. The study extends Buchdahl's original theorem by combining it with the Kerr-Schild representation. In doing so, we construct new vacuum-rotating black holes in higher dimensions which can be viewed as the Levi-Civita extensions of the Myers-Perry geometries. Furthermore, it demonstrates that the double copy scheme within these new generated geometries still holds, providing an example of an algebraically general double copy framework. In the context of the Einstein-Scalar system, the paper extends the corresponding Buchdahl theorem to scenarios where a static vacuum seed configuration, transformed with respect to a spacelike Killing vector, generates a hairy black hole spacetime. We analyze the geometrical features of these spacetimes and investigate how a change of frame, via conformal transformations, leads to a new family of black hole spacetimes within the Einstein-Conformal-Scalar system.

We adopt general relativistic ray-tracing (GRRT) schemes to study images of Kerr-MOG black holes surrounded by geometrically thick magnetized equilibrium tori, which belong to steady-state solutions of thick accretion disks within the framework of general relativistic magnetohydrodynamics (GRMHD). The black hole possesses an extra dimensionless MOG parameter described its deviation from usual Kerr one. Our results show that the presence of the MOG parameter leads to smaller disks in size, but enhances the total flux density and peak brightness in their images. Combining with observation data of black hole M87* from the Event Horizon Telescope (EHT), we make a constraint on parameters of the Kerr-MOG black hole and find that the presence of the MOG parameter broadens the allowable range of black hole spin.

We construct a (quantum mechanically) modified model for the Oppenheimer-Snyder collapse scenario where the exterior of the collapsing dust ball is a Hayward black hole spacetime and the interior is a dust Friedmann-Robertson-Walker cosmology. This interior cosmology is entirely determined by the junction conditions with the exterior black hole. It turns out to be non-singular, displaying a power-law contraction which precedes a de Sitter phase or, reversely, a power-law expansion followed by a de Sitter era. We also analyse the global causal structure and the viability of the model.

In the context of $f(R,T)$ gravity and other modified theories of gravity, the knowledge of the first order variation of the trace $T$ of the energy-momentum tensor with respect to the metric is essential for an accurate characterization of the gravitational field. In this paper, by considering a paradigmatic example of a perfect fluid whose dynamics is described by a pure k-essence matter Lagrangian in $f(R,T)=R+\mathcal F(T)$ gravity, we show that the first order variation of the trace of the energy-momentum tensor cannot in general be determined from the proper density, proper pressure and 4-velocity of the fluid alone, and that the sound speed of the fluid can directly influence the dynamics of gravity. We also confirm that the second variation of the matter Lagrangian with respect to the metric should not in general be neglected. These results can be particularly relevant for cosmological studies of $f(R,T)$ gravity in which some of the material content of the Universe is modeled as a perfect fluid.

Rapid formation of supermassive black holes occurs in dense nuclear star clusters that are initially gas-dominated. Stellar-mass black hole remnants of the most massive cluster sink into the core, where a massive runaway black hole forms as a consequence of combined effects of repeated mergers and Eddington-limited gas accretion. The associated gravitational-wave signals of high-redshift extreme mass-ratio inspirals are a unique signature of the nuclear star cluster scenario.

We propose precise effective field theory criteria to obtain a four-dimensional de Sitter space within M-theory. To this effect, starting with the state space described by the action of metric perturbations, fluxes etc over the supersymmetric Minkowski vacuum in eleven-dimensions, we discuss the most general low energy effective action in terms of the eleven-dimensional fields including non-perturbative and non-local terms. Given this, our criteria to obtain a valid four-dimensional de Sitter solution at far IR involve satisfying the Schwinger-Dyson equations of the associated path integral, as well as obeying positivity constraints on the dual IIA string coupling and its time derivative. For excited states, the Schwinger-Dyson equations imply an effective emergent potential different from the original potential. We show that while vacuum solutions and arbitrary coherent states fail to satisfy these criteria, a specific class of excited states called the Glauber-Sudarshan states obey them. Using the resurgent structure of observables computed using the path integral over the Glauber-Sudarshan states, four-dimensional de Sitter in the flat slicing can be constructed using a Glauber-Sudarshan state in M-theory. Among other novel results, we discuss the smallness of the positive cosmological constant, including the curious case where the cosmological constant is very slowly varying with time. We also discuss the resolution of identity with the Glauber-Sudarshan states, generation and the convergence properties of the non-perturbative and the non-local effects, the problems with the static patch and other related topics. We analyze briefly the issues related to the compatibility of the Wilsonian effective action with Borel resummations and discuss how they influence the effective field theory description in a four-dimensional de Sitter space.

The presence of an abundant population of low frequency photons at high redshifts (such as a radio background) can source leading order effects on the evolution of the matter and spin temperatures through rapid free-free absorptions. This effect, known as soft photon heating, can have a dramatic impact on the differential brightness temperature, $\Delta T_{\rm b}$, a central observable in $21$cm cosmology. Here, we introduce a semi-analytic framework to describe the dynamics of soft photon heating, providing a simplified set of evolution equations and a useful numerical scheme which can be used to study this generic effect. We also perform quasi-instantaneous and continuous soft photon injections to elucidate the different regimes in which soft photon heating is expected to impart a significant contribution to the global $21$cm signal and its fluctuations. We find that soft photon backgrounds produced after recombination with spectral index $\gamma > 3.0$ undergo significant free-free absorption, and therefore this heating effect cannot be neglected. The effect becomes stronger with steeper spectral index, and in some cases the injection of a synchrotron-like spectrum ($\gamma = 3.6$) can suppress the amplitude of $\Delta T_{\rm b}$ relative to the standard model prediction, making the global $21$cm signal even more difficult to detect in these scenarios.

This paper investigates the Casimir effect of a wedge and its holographic dual. We prove that the displacement operator universally determines the wedge Casimir effect in the smooth limit. Besides, we argue that the wedge Casimir energy increases with the opening angle and test it with several examples. Furthermore, we construct the holographic dual of wedges in AdS/BCFT in general dimensions. We verify that our proposal can produce universal relations within smooth and singular limits. We find that the negative brane tension tends to yield smaller wedge Casimir energy. Next, we discuss the wedge contribution to holographic entanglement entropy and find it increases with the opening angle, similar to the wedge Casimir energy. Finally, we briefly discuss the holographic polygon in AdS$_3$/BCFT$_2$ and its generalization to higher dimensions.

In this paper, we define a model of non-interacting quantum fields satisfying $(\Delta_g-\lambda^2)\phi=0$ on a Riemannian scattering space $(M,g)$ with two boundary components, i.e. a manifold with two asymptotically conic ends (meaning asymptotic to the "large end" of a cone). Our main result describes a canonical construction of two-point functions satisfying a version of the Hadamard condition.

Oscillating neutron stars are sources of continuous gravitational waves. We study analytically the excitation of stellar oscillations by the mechanical impact on the stellar surface of ''clumps'' of stochastically accreted matter. We calculate the waveform and spectrum of the gravitational wave signal emitted by the accretion-driven pulsations. Results are generated for an idealised model of a nonrotating, unmagnetised, one-component star with uniform polytropic index $n_{\rm poly}$ assuming Newtonian gravity and the Cowling approximation. We find that the excited mode amplitudes grow with increasing $n_{\rm poly}$ and mode order $n$. The gravitational wave signal forms a sequence of amplitude-modulated packets for $n_{\rm poly}=1$, lasting $\sim 10^{-3}$s after each impact. The gravitational wave strain increases with increasing $n_{\rm poly}$, but decreases with increasing $n$ and increasing multipole order $l$ for $n_{\rm poly}=1$. In the observing band of current long-baseline interferometers, $g$-modes emit higher, narrower peaks in the amplitude spectral density than $f$- and $p$-modes, with the highest peaks reaching $\sim 10^{-26}$Hz$^{-1/2}$ for modes with damping time $\tau_{nl} \sim 10^{8}$yr. The root-mean-square strain $h_{\text{rms}}$, calculated by summing over modes with $2\leq l\leq4$ and $\tau_{nl} \leq 10^{8}$yr, spans the range $10^{-33} \leq h_{\text{rms}} \leq 10^{-32}$ for $1\leq n_{\text{poly}}\leq 2$.

Recently, there has been a growing interest in celestial holography, which is holography in asymptotic flat spacetimes. This holographic duality exhibits numerous mysterious and fruitful features, particularly on the dual CFT side. In this paper, we present the candidate of dual CFT of Minkowski spacetime extracted from $SL(2,\mathbb{C})/SU(2)\cong H^+_3$ Wess-Zumino-Witten (WZW) model, the simplest non-compact CFT. We demonstrate that it reproduces the well-known principal series and correlation functions dual to the bulk scattering amplitudes.

We investigate the impact of the Dark Energy Spectroscopic Instrument (DESI) 2024 data on dark energy scenarios. We thus analyze three typologies of models, the first in which the cosmic speed up is related to thermodynamics, the second associated with Taylor expansions of the barotropic factor, whereas the third based on \emph{ad hoc} dark energy parameterizations. In this respect, we perform Monte Carlo Markov chain analyses, adopting the Metropolis-Hastings algorithm, of 12 models. To do so, we first work at the background, inferring \emph{a posteriori} kinematic quantities associated with each model. Afterwards, we obtain early time predictions, computing departures on the growth evolution with respect to the model that better fits DESI data. We find that the best model to fit data \emph{is not} the Chevallier-Polarski-Linder (CPL) parametrization, but rather a more complicated log-corrected dark energy contribution. To check the goodness of our findings, we further directly fit the product, $r_d h_0$, concluding that $r_d h_0$ is anticorrelated with the mass. This treatment is worked out by removing a precise data point placed at $z=0.51$. Surprisingly, in this case the results again align with the $\Lambda$CDM model, \emph{indicating that the possible tension between the concordance paradigm and the CPL model can be severely alleviated}. We conclude that future data points will be essential to clarify whether dynamical dark energy is really in tension with the $\Lambda$CDM model.

We study the Schr\"odinger equation in quantum field theory (QFT) in its functional formulation. In this approach quantum correlation functions can be expressed as classical expectation values over (complex) stochastic processes. We obtain a stochastic representation of the Schr\"odinger time evolution on Wentzel-Kramers-Brillouin (WKB) states by means of the Wiener integral. We discuss QFT in a flat expanding metric and in de Sitter space-time. We calculate the evolution kernel in an expanding flat metric in the real time formulation. We discuss a field interaction in pseudoRiemannian and Riemannian metrics showing that an inversion of the signature leads to some substantial simplifications of the singularity problems in QFT.

We employ Hubble data and Gaussian Processes in order to reconstruct the dynamical connection function in $f(Q)$ cosmology beyond the coincident gauge. In particular, there exist three branches of connections that satisfy the torsionless and curvatureless conditions, parameterized by a new dynamical function $\gamma$. We express the redshift dependence of $\gamma$ in terms of the $H(z)$ function and the $f(Q)$ form and parameters, and then we reconstruct it using 55 $H(z)$ observation data. Firstly, we investigate the case where ordinary conservation law holds, and we reconstruct the $f(Q)$ function, which is very well described by a quadratic correction on top of Symmetric Teleparallel Equivalent of General Relativity. Proceeding to the general case, we consider two of the most studied $f(Q)$ models of the literature, namely the square-root and the exponential one. In both cases we reconstruct $\gamma(z)$, and we show that according to AIC and BIC information criteria its inclusion is favoured compared to both $\Lambda$CDM paradigm, as well as to the same $f(Q)$ models under the coincident gauge. This feature acts as an indication that $f(Q)$ cosmology should be studied beyond the coincident gauge.

We discuss the challenges that the standard (Humean and non-Humean) accounts of laws face within the framework of quantum gravity where space and time may not be fundamental. This paper identifies core (meta)physical features that cut across a number of quantum gravity approaches and formalisms and that provide seeds for articulating updated conceptions that could account for QG laws not involving any spatio-temporal notions. To this aim, we will in particular highlight the constitutive roles of quantum entanglement, quantum transition amplitudes and quantum causal histories. These features also stress the fruitful overlap between quantum gravity and quantum information theory.

We propose a novel method (floZ), based on normalizing flows, for estimating the Bayesian evidence (and its numerical uncertainty) from a set of samples drawn from the unnormalized posterior distribution. We validate it on distributions whose evidence is known analytically, up to 15 parameter space dimensions, and compare with two state-of-the-art techniques for estimating the evidence: nested sampling (which computes the evidence as its main target) and a k-nearest-neighbors technique that produces evidence estimates from posterior samples. Provided representative samples from the target posterior are available, our method is more robust to posterior distributions with sharp features, especially in higher dimensions. It has wide applicability, e.g., to estimate the evidence from variational inference, Markov-chain Monte Carlo samples, or any other method that delivers samples from the unnormalized posterior density.

Year 1 results of the Legacy Survey of Space and Time (LSST) will provide tighter constraints on small-scale cosmology, beyond the validity of linear perturbation theory. This heightens the demand for a computationally affordable prescription that can accurately capture nonlinearities in beyond-$\Lambda$CDM models. The COmoving Lagrangian Acceleration (COLA) method, a cost-effective \textit{N}-body technique, has been proposed as a viable alternative to high-resolution \textit{N}-body simulations for training emulators of the nonlinear matter power spectrum. In this study, we evaluate this approach by employing COLA emulators to conduct a cosmic shear analysis with LSST-Y1 simulated data across three different nonlinear scale cuts. We use the $w$CDM model, for which the \textsc{EuclidEmulator2} (\textsc{ee2}) exists as a benchmark, having been trained with high-resolution \textit{N}-body simulations. We primarily utilize COLA simulations with mass resolution $M_{\rm part}\approx 8 \times 10^{10} ~h^{-1} M_{\odot}$ and force resolution $\ell_{\rm force}=0.5 ~h^{-1}$Mpc, though we also test refined settings with $M_{\rm part}\approx 1 \times 10^{10} ~h^{-1}M_{\odot}$ and force resolution $\ell_{\rm force}=0.17 ~h^{-1}$Mpc. We find the performance of the COLA emulators is sensitive to the placement of high-resolution \textit{N}-body reference samples inside the prior, which only ensure agreement in their local vicinity. However, the COLA emulators pass stringent criteria in goodness-of-fit and parameter bias throughout the prior, when $\Lambda$CDM predictions of \textsc{ee2} are computed alongside every COLA emulator prediction, suggesting a promising approach for extended models.

Measurements of the luminosity distance of propagating gravitational waves can provide invaluable information on the geometry and content of our Universe. Due to the clustering of cosmic structures, in realistic situations we need to average the luminosity distance of events coming from patches inside a volume. In this work we evaluate, in a gauge-invariant and fully-relativistic treatment, the impact of cosmological perturbations on such averaging process. We find that clustering, lensing and peculiar velocity effects impact estimates for future detectors such as Einstein Telescope, Cosmic Explorer, the Big Bang Observer and DECIGO. The signal-to-noise ratio of the angular power spectrum of the average luminosity distance over all the redshift bins is 17 in the case of binary black holes detected by Einstein Telescope and Cosmic Explorer. We also provide fitting formulas for the corrections to the average luminosity distance due to general relativistic effects.