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To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions., Comment: Collection of summaries of twelve topical panel discussions and individual thoughts of speakers and panelists, Nordita Scientific Program "Quantum Gravity: from gravitational EFTs to UV complete approaches". 62 pages + references, no figures

It is notoriously difficult to construct a stable non-singular bouncing cosmology that avoids all possible instabilities throughout the entire evolution of the universe. In this work, we explore whether a non-singular bounce driven by a specific class of modifications of General Relativity, the vector-tensor generalized Proca theories, can be constructed without encountering any pathologies in linear perturbation theory. We find that such models unavoidably lead to either an instability in the matter sector or strong coupling in the scalar one. As our analysis is performed in a gauge-independent way, this result can be cast in the form of a no-go theorem for non-singular bounces with generalized Proca. In contrast to the no-go theorem found for Horndeski theories, however, it cannot be evaded by considering beyond generalized Proca theory. At the core of our result lies the non-dynamical nature of the temporal component of the vector field, which renders it an ill-suited mediator for a bouncing solution., Comment: 14 pages, no figures

We consider evolving, spatially flat isotropic and homogeneous (FLRW) cosmologies in ghost-free (dRGT) massive gravity. In this theory, no dynamical flat FLRW background exists if the reference metric is chosen to be Minkowski and the Stueckelberg fields are homogeneous. Relaxing the assumptions on the Stueckelberg profiles gives access to dynamical backgrounds. We propose a classification of the viable flat FLRW cosmological solutions of dRGT massive gravity. Instead of specifying an initial ansatz for the Stueckelberg fields $\phi^a$ and the reference metric $f_{ab}$, we show that imposing homogeneity and isotropy on the square root tensor $X^{\mu}_{\nu}=\left(\sqrt{g^{-1}\partial\phi^a \partial\phi^bf_{ab}}\right)^{\mu}_{\nu}$ leads to dynamical cosmological solutions, and we characterize their properties. These solutions become dynamical only when the Stueckelberg fields acquire a sufficiently inhomogeneous and/or anisotropic profile. We explore the consequences for the minimal model and the complete dRGT theory, and show that perturbations are strongly coupled, at the quadratic level, on these backgrounds., Comment: 30 pages, 2 figures

We assess the prospects for detecting gravitational wave echoes arising due to the quantum nature of black hole horizons with LISA. In a recent proposal, Bekenstein's black hole area quantization is connected to a discrete absorption spectrum for black holes in the context of gravitational radiation. Consequently, for incoming radiation at the black hole horizon, not all frequencies are absorbed, raising the possibility that the unabsorbed radiation is reflected, producing an echo-like signal closely following the binary coalescence waveform. In this work, we further develop this proposal by introducing a robust, phenomenologically motivated model for black hole reflectivity. Using this model, we calculate the resulting echoes for an ensemble of Numerical Relativity waveforms and examine their detectability with the LISA space-based interferometer. Our analysis demonstrates promising detection prospects and shows that, upon detection, LISA provides a direct probe of the Bekenstein-Hawking entropy. In addition, we find that the information extractable from LISA data offers valuable constraints on a wide range of quantum gravity theories., Comment: 9 pages, 8 Figures

The superradiant growth of massive vector fields in rotating black hole spacetimes has garnered significant attention in recent literature. However, the majority of these studies overlook the influence of a cosmological constant, which likely constitutes the primary energy content of our universe. In this paper, we extend recent research by incorporating a cosmological constant into the Einstein+Proca system and numerically evolving the resulting equations of motion. Utilizing the newly released GRBoondi numerical relativity code, designed specifically for the numerical evolution of (generalized) Proca fields, we discover that parameters causing a growing instability in the $\Lambda = 0$ scenario transition to a decaying state when $\Lambda > 0$. This results in a more intriguing phenomenology. These simulations pave the way for future full Einstein+Proca simulations to explore the secular decay of the resultant cloud from gravitational emission.

Gravitational wave (GW) astronomy has revolutionized our capacity to explore nature. The next generation of observatories, among which the space-borne detector Laser Interferometer Space Antenna LISA, is expected to yield orders of magnitude of signal-to-noise ratio improvement, and reach fainter and novel features of General Relativity. Among them, an exciting possibility is the detection of GW memory. Interpreted as a permanent deformation of the background spacetime after a GW perturbation has passed through the detector, GW memory offers a novel avenue to proof-test General Relativity, access the non-linear nature of gravity, and provide complementary information to better characterize the GW source. Previous studies have shown that GW memory detection from individual mergers of massive black hole binaries is expected with LISA. However, these works have not simulated the proper time domain response of the detector to the GW memory. This work is filling this gap and presents the detection prospects of LISA regarding GW memory and the expected signature of GW memory on the data-streams using the most up-to-date LISA consortium simulations of the response. We focus on the GW memory of massive black hole binary mergers and use state-of-the-art population models to assess the likelihood of detecting the GW memory within the LISA lifetime. We conclude that GW memory will be a key feature of several events detected by LISA, and will help to exploit the scientific potential of the mission fully., Comment: 19 pages, 15 figures. v2 structure of document and modeling of memory signal revised, with extra clarifications. Main results and conclusions unchanged

While numerical simulations offer unparalleled precision and robustness in studying complex physical systems, their execution is often hindered by complexity, costliness, and time consumption due to the intricate equations involved. This challenge is already encountered in General Relativity, where non-flat spacetimes exacerbate the computational burden. This complexity is further intensified when dealing with additional degrees of freedom. To address this challenge head-on, we introduce GRBoondi, a groundbreaking fixed-background numerical relativity code designed to provide a unified interface for numerically solving Generalized Proca theories. GRBoondi grants users the ability to make arbitrary modifications to the Proca equations of motion on any background, providing a robust and versatile tool for exploring diverse classes of Generalized Proca theories. This letter serves as part of the submission of GRBoondi to the Journal of Open Source Software. For access to the code, please visit https://github.com/ShaunFell/GRBoondi.git., Comment: Submitted for review in the Journal of Open Source Software; Comments welcome; The code can be found at https://github.com/ShaunFell/GRBoondi.git

We perform a comprehensive analysis of state-of-the-art waveform models, focusing on their predictions concerning kick velocity and inferred gravitational wave memory. In our investigation we assess the accuracy of waveform models using energy-momentum balance laws, which were derived in the framework of full, non-linear General Relativity. The numerical accuracy assessment is performed for precessing as well as non-precessing scenarios for models belonging to the \textit{EOB}, \textit{Phenom}, and \textit{Surrogate} families. We analyze the deviations of these models from each other and from Numerical Relativity waveforms. Our analysis reveals statistically significant deviations, which we trace back to inaccuracies in modelling subdominant modes and inherent systematic errors in the chosen models. We corroborate our findings through analytical considerations regarding the mixing of harmonic modes in the computed kick velocities and inferred memories., Comment: 22 pages, 15 figures, Comments are welcome

We propose a diagnostic tool for future analyses of stochastic gravitational wave background signals of extra-galactic origin in LISA data. Next-generation gravitational wave detectors hold the capability to track unresolved gravitational waves bundled into a stochastic background. This composite background contains cosmological and astrophysical contributions, the exploration of which offers promising avenues for groundbreaking new insights into very early universe cosmology as well as late-time structure formation. In this article, we develop a full end-to-end pipeline for the extraction of extra-galactic signals, based on kinematic anisotropies arising from the galactic motion, via full-time-domain simulations of LISA's response to the gravitational wave anisotropic sky. Employing a Markov-Chain-Monte-Carlo map-making scheme, multipoles up to $\ell=2$ are recovered for scale-free spectra that support an interpretation as signals originating from cosmic strings in the case of a high signal-to-noise ratio. We demonstrate that our analysis is consistently beating cosmic variance and is robust against statistical and systematic errors. The impact of instrumental noise on the extraction of kinematic anisotropies is investigated, and we establish a detection threshold of $\Omega_{GW}\gtrsim 5\times 10^{-8}$ in the presence of instrument-induced noise. Potential avenues for improvement in our methodology are highlighted., Comment: 18 pages, 11 figures

We delve into the first-order thermodynamics of Horndeski gravity, focusing on spatially flat, homogeneous, and isotropic cosmologies. Our exploration begins with a comprehensive review of the effective fluid representation within viable Horndeski gravity. Notably, we uncover a surprising alignment between the constitutive relations governing the "Horndeski fluid" and those of Eckart's thermodynamics. Narrowing our focus, we specialize our discussion to spatially flat Friedmann-Lema{\^i}tre-Robertson-Walker spacetimes. Within this specific cosmological framework, we systematically analyze two classes of theories: shift-symmetric and asymptotically shift-symmetric. These theories are characterized by a non-vanishing braiding parameter, adding a nuanced dimension to our investigation. On the one hand, unlike the case of the "traditional" scalar-tensor gravity, these peculiar subclasses of viable Horndeski gravity never relax to General Relativity (seen within this formalism as an equilibrium state at zero temperature), but give rise to additional equilibrium states with non-vanishing viscosity. On the other hand, this analysis further confirms previous findings according to which curvature singularities are "hot" and exhibit a diverging temperature, which suggests that deviations of scalar-tensor theories from General Relativity become extreme at spacetime singularities. Furthermore, we provide a novel exact cosmological solution for an asymptotically shift-symmetric theory as a toy model for our thermodynamic analysis., Comment: 16 pages. Matches published version in Phys. Rev. D

Based on a recently proposed reinterpretation of gravitational wave memory that builds up on the definition of gravitational waves pioneered by Isaacson, we provide a unifying framework to derive both ordinary and null memory from a single well-defined equation at leading order in the asymptotic expansion. This allows us to formulate a memory equation that is valid for any unbound asymptotic energy-flux that preserves local Lorentz invariance. Using Horndeski gravity as a concrete example metric theory with an additional potentially massive scalar degree of freedom in the gravitational sector, the general memory formula is put into practice by presenting the first account of the memory correction sourced by the emission of massive field waves. Throughout the work, physical degrees of freedom are identified by constructing manifestly gauge invariant perturbation variables within an SVT decomposition on top of the asymptotic Minkowski background, which will in particular prove useful in future studies of gravitational wave memory within vector tensor theories., Comment: 17 pages. v2 contains a fix of a computation error. Comments are welcome

We study linear cosmological perturbations in the most general teleparallel gravity setting, where gravity is mediated by the torsion and nonmetricity of a flat connection alongside the metric. For a general linear perturbation of this geometry around a homogeneous and isotropic background geometry, we derive the irreducible decomposition of the perturbation variables, as well as their behavior under gauge transformations, i.e., infinitesimal diffeomorphisms generated by a vector field. In addition, we also study these properties for the most general set of matter variables and gravitational field equations. We then make use of these result to construct gauge-invariant perturbation variables, using a general approach based on gauge conditions. We further calculate these quantities also in the metric and symmetric teleparallel geometries, where nonmetricity or torsion is imposed to vanish. To illustrate our results, we derive the energy-momentum-hypermomentum conservation equations for both the cosmological background and the linear perturbations. As another example, we study the propagation of tensor perturbations in the $f(G)$, $f(T)$ and $f(Q)$ class of theories., Comment: 23 pages, no figures; some corrections

There has been growing interest in $f(Q)$ gravity, which has led to significant advancements in the field. However, it is important to note that most studies in this area were based on the coincident gauge, thus overlooking the impact of the connection degrees of freedom. In this work, we pay special attention to the connection when studying perturbations in general teleparallel, metric teleparallel, and symmetric teleparallel theories of gravity. We do not just examine perturbations in the metric, but also in the affine connection. To illustrate this, we investigate cosmological perturbations in $f(G)$, $f(T)$, and $f(Q)$ gravity with and without matter in form of an additional scalar field for spatially flat and curved FLRW geometries. Our perturbative analysis reveals that for general $f(Q)$ backgrounds, there are up to seven degrees of freedom, depending on the background connection. This is in perfect agreement with the upper bound on degrees of freedom established for the first time in $\href{https://doi.org/10.1002/prop.202300185}{Fortschr. Phys. 2023, 2300185}$. In $f(G)$ and $f(T)$ gravity theories, only two tensor modes propagate in the gravity sector on generic curved cosmological backgrounds, indicating strong coupling problems. In the context of $f(Q)$ cosmology, we find that for a particular background connection, where all seven modes propagate, there is at least one ghost degree of freedom. For all other choices of the connection the ghost can be avoided at the cost of strong coupling problem, where only four degrees of freedom propagate. Hence, all of the cosmologies within the teleparallel families of theories in form of $f(G)$, $f(T)$, and $f(Q)$ suffer either from strong coupling or from ghost instabilities. A direct coupling of the matter field to the connection or non-minimal couplings might alter these results., Comment: 63 pages, comments are very welcome

Recent years have witnessed a rise in interest in the geometrical trinity of General Relativity and its extensions. This interest has been fuelled by novel insights into the nature of gravity, the possibility to address computational and conceptual questions -- such as the determination of black hole entropy or the definition of gravitational energy-momentum -- from a new perspective. In particular, $f(Q)$ gravity has also inspired numerous works on black holes, wormholes, and cosmology. In the latter case, $f(Q)$ models have the potential to elucidate phenomena in both early and late-time cosmology without necessitating the inclusion of dark energy, the inflaton field, or dark matter. Particularly noteworthy is the role of $f(Q)$ theories in addressing cosmological tensions, presenting exciting possibilities for reshaping our understanding of gravity and its manifestations in cosmology. The emergence of intriguing new black hole solutions and the potential existence of wormhole solutions suggest the presence of novel physics within the realm of strong gravity. These phenomena have become increasingly measurable only in recent times, opening up exciting avenues for further exploration and discovery. This review is tailored to students and researchers alike. It offers a self-contained and pedagogical introduction to metric-affine geometry--The mathematical foundation and indispensable tool upon which the geometrical trinity of General Relativity as well as its various extensions are built., Comment: 106 pages, 13 figures, 2 tables. Comments are welcome! Please write us if we forgot to cite your important works. Apologies!

Gravitational waveforms play a crucial role in comparing observed signals to theoretical predictions. However, obtaining accurate analytical waveforms directly from general relativity remains challenging. Existing methods involve a complex blend of post-Newtonian theory, effective-one-body formalism, numerical relativity, and interpolation, introducing systematic errors. As gravitational wave astronomy advances with new detectors, these errors gain significance, particularly when testing general relativity in the non-linear regime. A recent development proposes a novel approach to address this issue. By deriving precise constraints - or balance laws - directly from full non-linear GR, this method offers a means to evaluate waveform quality, detect template weaknesses, and ensure internal consistency. Before delving into the intricacies of balance laws in full non-linear general relativity, we illustrate the concept using a detailed mechanical analogy. We'll examine a dissipative mechanical system as an example, demonstrating how mechanical balance laws can gauge the accuracy of approximate solutions in capturing the complete physical scenario. While mechanical balance laws are straightforward, deriving balance laws in electromagnetism and general relativity demands a rigorous foundation rooted in mathematically precise concepts of radiation. Following the analogy with electromagnetism, we derive balance laws in general relativity. As a proof of concept, we employ an analytical approximate waveform model, showcasing how these balance laws serve as a litmus test for the model's validity., Comment: 26 pages, 14 figues. Comments are welcome!

Gravitational-wave interferometers have been recently proposed as a promising probe in searches for dark matter. These highly sensitive instruments are potentially able to detect the interactions of dark matter with the detector's hardware. In this work, we explore the possibilities of discovering topological dark matter with the LIGO detectors. We analyze domain walls consisting of dark matter passing through the Earth, leaving traces in multiple detectors simultaneously. Considering dark matter interactions with light in the interferometer, and with the beam splitter, we perform the first analysis of topological dark matter with gravitational-wave strain data. We examine whether astrophysically unexpected triggers could be explained by domain-wall passages. We find that all of the binary black hole mergers we analyze favor the binary black hole merger hypothesis rather than the domain-wall hypothesis, with the closest being GW190521. Moreover, we find that some topological dark matter signals can be caught by binary black hole searches. Finally, we find that special types of glitches in the measurement data can inevitably limit the dark matter searches for certain parameters. These results are expected to guide future searches and analyses., Comment: 16 pages with 14 figures

In recent years, $f(Q)$ gravity has enjoyed considerable attention in the literature and important results have been obtained. However, the question of how many physical degrees of freedom the theory propagates -- and how this number may depend on the form of the function $f$ -- has not been answered satisfactorily. In this article we show that a Hamiltonian analysis based on the Dirac-Bergmann algorithm -- one of the standard methods to address this type of question -- fails. We isolate the source of the failure, show that other commonly considered teleparallel theories of gravity are affected by the same problem, and we point out that the number of degrees of freedom obtained in Phys. Rev. D 106 no. 4, (2022) by K. Hu, T. Katsuragawa, and T. Qui (namely eight), based on the Dirac-Bergmann algorithm, is wrong. Using a different approach, we show that the upper bound on the degrees of freedom is seven. Finally, we propose a more promising strategy for settling this important question., Comment: 45 pages, 3 figues, Comments are welcome

The Laser Interferometer Space Antenna (LISA), space-based gravitational wave observatory involves a complex multidimensional closed-loop dynamical system. Its instrument performance is expected to be less efficiently isolated from platform motion than was its simpler technological demonstrator, LISA Pathfinder. It is of crucial importance to understand and model LISA dynamical behavior accurately to understand the propagation of dynamical excitations through the response of the instrument down to the interferometer data streams. More generally, simulation of the system allows for the preparation of the processing and interpretation of in-flight metrology data. In this work, we present a comprehensive mathematical modeling of the closed-loop system dynamics and its numerical implementation within the LISA Consortium simulation suite. We provide, for the first time, a full time-domain numerical demonstration of post-processing Time Delay Interferometer techniques combining multiple position measurements with realistic control loops to create a synthetic Michelson interferometer. We show that in the absence of physical coupling to spacecraft and telescope motion (through tilt-to-length, stiffness and actuation cross-talk) the effect of noisy spacecraft motion is efficiently suppressed to a level below the noise originating in the rest of the instrument., Comment: 26 pages, 8 figures. Revision of Subsection VII.C, and of the physical interpretation of the comparison between Linear and Non-linear simulations. In addition to a few editorial improvements (rephrasings, figure and text formatting). The dynamical models, the simulations, and the results of the article (aside from VII.C) remain unchanged

The advent of gravitational wave astronomy has seen a huge influx of new predictions for potential discoveries of beyond the Standard Model fields. The coupling of all fundamental fields to gravity, together with its dominance on large scales, makes gravitational physics a rich laboratory to study fundamental physics. This holds especially true for the search for the elusive dark photon, a promising dark matter candidate. The dark photon is predicted to generate instabilities in a rotating black hole spacetime, birthing a macroscopic Bose-Einstein condensate. These condensates can especially form around super massive black holes, modifying the dynamical inspiralling process. This then opens another window to leverage future space-borne gravitational wave antennas to join the hunt for the elusive dark matter particle. This study builds a preliminary model for the gravitational waveform emitted by such a dressed extreme mass-ratio inspiral. Comparing these waveforms to the vacuum scenario allows projections to the potential constrainability on the dark photon mass by space-borne gravitational wave antennas. The superradiant instability of a massive vector field on a Kerr background is calculated and, under reasonable approximations, the backreaction on the orbit of an inspiralling solar mass-scale compact object due to the secular evolution of the resulting boson cloud is determined. The end result is the projection that the LISA mission should be able to constrain the dark photon mass using extreme mass ratio inspirals in the range $[1.8 \times 10^{-17}, 4.47 \times 10^{-16}]$ eV., Comment: 21 Pages, 8 Figures

The merger remnant of a binary neutron star coalescence is initially strongly differentially rotating. Some properties of these remnants can be accurately modeled through building equilibrium neutron star models. In the present paper, we study how a modification of general relativity, namely scalar-tensor theory with a massive scalar field, will alter the picture. In contrast to previous studies, we implement a realistic phenomenological differential rotational law which allows for neutron star models to attain maximal angular velocity away from the center. We find that solutions with much higher masses and angular momenta exist in scalar-tensor theory compared to general relativity. They keep their quasi-spherical energy-density distribution for significantly higher values of the angular momentum before transitioning to quasi-toroidal models, in contrast to pure general relativity. Constructing such neutron star solutions is the first step to our final goal that is studying how scalarization alters the stability and gravitational wave emission of post-merger remnants., Comment: 17 pages, 6 figures

It has recently been argued that half degrees of freedom could emerge in Lorentz and parity invariant field theories, using a non-linear Proca field theory dubbed Proca-Nuevo as a specific example. We provide two proofs, using the Lagrangian and Hamiltonian pictures, that the theory possesses a pair of second class constraints, leaving $D-1$ degrees of freedom in $D$ spacetime dimensions, as befits a consistent Proca model. Our proofs are explicit and straightforward in two dimensions and we discuss how they generalize to an arbitrary number of dimensions. We also clarify why local Lorentz and parity invariant field theories cannot hold half degrees of freedom.

Gravitational wave memory is a nonoscillatory correction to the gravitational wave strain predicted by general relativity, which has yet to be detected. Within general relativity, its dominant component, known as the null memory, can be understood as arising from the backreaction of the energy carried by gravitational waves, and therefore it corresponds to a direct manifestation of the nonlinearity of the theory. In this paper, we investigate the null-memory prediction in a broad class of modified gravity theories, with the aim of exploring potential lessons to be learned from future measurements of the memory effect. Based on Isaacson's approach to the leading-order field equations, we in particular compute the null memory for the most general scalar-vector-tensor theory with second-order equations of motion and vanishing field potentials. We find that the functional form of the null memory is only modified through the potential presence of additional radiative null energy sources in the theory. We subsequently generalize this result by proving a theorem that states that the simple structure of the tensor null-memory equation remains unaltered in any metric theory whose massless gravitational fields satisfy decoupled wave equations to first order in perturbation theory, which encompasses a large class of viable extensions to general relativity., Comment: 39 pages

Motivated by a version of the ``Dipolar Dark Matter'' model, that aims at a relativistic completion of the phenomenology of MOND, we investigate the gravitational polarization mechanism in the canonical bimetric theory with an effective matter coupling. We explicitly show the fundamental obstacle why such theories cannot achieve a consistent gravitational polarization, and thus fail to recover the MONDian phenomenology at low energies., Comment: 8 pages

We derive the most general homogeneous and isotropic teleparallel geometries, defined by a metric and a flat, affine connection. We find that there are five branches of connection solutions, which are connected via several limits, and can further be restricted to the torsion-free and metric-compatible cases. We apply our results to several classes of general teleparallel gravity theories and derive their cosmological dynamics for all five branches. Our results show that for large subclasses of these theories the dynamics reduce to that of closely related metric or symmetric teleparallel gravity theories, while for other subclasses up to two new scalar degrees of freedom participate in the cosmological dynamics., Comment: 21 pages, 1 figure

Non-linear cosmic structures contain valuable information on the expansion history of the background space-time, the nature of dark matter, and the gravitational interaction. The recently developed kinetic field theory of cosmic structure formation (KFT) allows to accurately calculate the non-linear power spectrum of cosmic density fluctuations up to wave numbers of $k\lesssim10\,h\,\mathrm{Mpc}^{-1}$ at redshift zero. Cosmology and gravity enter this calculation via two functions, viz. the background expansion function and possibly a time-dependent modification of the gravitational coupling strength. The success of the cosmological standard model based on general relativity suggests that cosmological models in generalized theories of gravity should have observable effects differing only weakly from those in standard cosmology. Based on this assumption, we derive the functional, first-order Taylor expansion of the non-linear power spectrum of cosmic density fluctuations obtained from the mean-field approximation in KFT in terms of the expansion function and the gravitational coupling strength. This allows us to study non-linear power spectra expected in large classes of generalized gravity theories. To give one example, we apply our formalism to generalized Proca theories., Comment: Accepted for publication in JCAP. v2: Added some clarifying remarks and further citations. In particular new section 5, in which this work is compared to other works on the same topic. Journal of Cosmology and Astroparticle Physics, Volume 2023, Issue 07, id.029, 19 pp. doi:10.1088/1475-7516/2023/07/029

Assuming unitarity, locality, causality, and Lorentz invariance of the, otherwise unknown, UV completion, we derive a new set of constraints on the effective field theory coefficients for the most general, ghost-free Generalized Proca and Proca Nuevo massive vector models. For the Generalized Proca model, we include new interactions that had not been previously considered in the context of positivity bounds and find these additional terms lead to a widened parameter space for the previously considered interactions. Although, the Generalized Proca and Proca Nuevo models are inequivalent, we find interesting analogues between the coefficients parameterizing the two models and the roles they play in the positivity bounds., Comment: 40 pages, 9 figures, 1 table, references and funding agencies updated

We give a detailed exposition of the formalism of Kinetic Field Theory (KFT) with emphasis on the perturbative determination of observables. KFT is a statistical non-equilibrium classical field theory based on the path integral formulation of classical mechanics, employing the powerful techniques developed in the context of quantum field theory to describe classical systems. Unlike previous work on KFT, we perform the integration over the probability distribution of initial conditions in the very last step. This significantly improves the clarity of the perturbative treatment and allows for physical interpretation of intermediate results. We give an introduction to the general framework, but focus on the application to interacting $N$-body systems. Specializing the results to cosmic structure formation, we reproduce the linear growth of the cosmic density fluctuation power spectrum on all scales from microscopic, Newtonian particle dynamics alone., Comment: 59 pages, 4 figures

The equivalence principle and its universality enables the geometrical formulation of gravity. In the standard formulation of General Relativity \'a la Einstein, the gravitational interaction is geometrized in terms of the spacetime curvature. However, if we embrace the geometrical character of gravity, two alternative, though equivalent, formulations of General Relativity emerge in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity. The latter allows a much simpler formulation of General Relativity oblivious to the affine spacetime structure, the Coincident General Relativity. The entropy of a black hole can be computed using the Euclidean path integral approach, which strongly relies on the addition of boundary or regulating terms in the standard formulation of General Relativity. A more fundamental derivation can be performed using Wald's formula, in which the entropy is directly related to Noether charges and is applicable to general theories with diffeomorphism invariance. In this work we extend Wald's Noether charge method for calculating black hole entropy to spacetimes endowed with non-metricity. Using this method, we show that Coincident General Relativity with an improved action principle gives the same entropy as the well-known entropy in standard General Relativity. Furthermore the first law of black hole thermodynamics holds and an explicit expression for the energy appearing in the first law is obtained., Comment: 30 pages

We analyze the properties that any late-time modification of the $\Lambda$CDM expansion history must have in order to consistently solve both the $H_0$ and the $\sigma_8$ tensions. Taking a model-independent approach, we obtain a set of necessary conditions that can be applied to generic late-time extensions. Our results are fully analytical and merely based on the assumptions that the deviations from the $\Lambda$CDM background remain small. For the concrete case of a dark energy fluid with equation of state $w(z)$, we derive the following general requirements: (i) Solving the $H_0$ tension demands $w(z)<-1$ at some $z$ (ii) Solving both the $H_0$ and $\sigma_8$ tensions requires $w(z)$ to cross the phantom divide. Finally, we also allow for small deviations on the effective gravitational constant. In this case, our method is still able to constrain the functional form of these deviations., Comment: 15 pages, 6 figures. Companion paper to arXiv:2201.11623

These notes provide a student-friendly introduction to the theory of gravitational waves in full, non-linear general relativity (GR). We aim for a balance between physical intuition and mathematical rigor and cover topics such as the Newman-Penrose formalism, electromagnetic waves, asymptotically Minkowski spacetimes, the peeling theorem, the universal structure of null infinity, the Bondi-Metzner-Sachs group, and the definition of radiative modes in linear as well as in non-linear GR. Many exercises and some explicitly calculated examples complement the abstract theory and are designed to help students build up their intuition and see the mathematical machinery at work., Comment: 127 pages, 12 figures

In a model independent approach, we derive generic conditions that any late time modification of the $\Lambda$CDM expansion history must satisfy in order to consistently solve both the $H_0$ and the $\sigma_8$ tensions. Our results are fully analytical and the method is merely based on the assumption that the late-time deviations from $\Lambda$CDM remain small. For the concrete case of a dark energy fluid with deviations encoded in the expansion history and the gravitational coupling constant, we present necessary conditions on its equation of state. Solving both the $H_0$ and $\sigma_8$ tensions requires that $w(z)$ must cross the phantom divide if $G_\text{eff}=G$. On the other hand, for $G_\text{eff}=G+\delta G(z)$ and $w(z)\leq -1$, it is required that $\displaystyle \frac{\delta G(z)}{G}<\alpha(z)\frac{\delta H(z)}{H(z)}<0$ at some redshift $z$., Comment: 4 pages, 2 figures, submission to PRL

We investigate the physical measurability of the infrared instability of a de Sitter phase in the formalism recently proposed by Kitamoto et al.. We find that the logarithmic decay of the effective cosmological constant is only measurable if an additional clock field is introduced., Comment: 9 pages