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The Cosmological Principle (CP) -- the notion that the Universe is spatially isotropic and homogeneous on large scales -- underlies a century of progress in cosmology. It is conventionally formulated through the Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies as the spacetime metric, and culminates in the successful and highly predictive $\Lambda$-Cold-Dark-Matter ($\Lambda$CDM) model. Yet, tensions have emerged within the $\Lambda$CDM model, most notably a statistically significant discrepancy in the value of the Hubble constant, $H_0$. Since the notion of cosmic expansion determined by a single parameter is intimately tied to the CP, implications of the $H_0$ tension may extend beyond $\Lambda$CDM to the CP itself. This review surveys current observational hints for deviations from the expectations of the CP, highlighting synergies and disagreements that warrant further study. Setting aside the debate about individual large structures, potential deviations from the CP include variations of cosmological parameters on the sky, discrepancies in the cosmic dipoles, and mysterious alignments in quasar polarizations and galaxy spins. While it is possible that a host of observational systematics are impacting results, it is equally plausible that precision cosmology may have outgrown the FLRW paradigm, an extremely pragmatic but non-fundamental symmetry assumption., Comment: extended contents and references, 73 pages (excluding references), 30 figures, version accepted for publication in Class. Quant. Grav. "Focus issue on the Hubble constant tension"

In this work we study the long-lived post-merger gravitational wave signature of a boson-star binary coalescence. We use full numerical relativity to simulate the post-merger and track the gravitational afterglow over an extended period of time. We implement recent innovations for the binary initial data, which significantly reduce spurious initial excitations of the scalar field profiles, as well as a measure for the angular momentum that allows us to track the total momentum of the spatial volume, including the curvature contribution. Crucially, we find the afterglow to last much longer than the spin-down timescale. This prolonged gravitational wave afterglow provides a characteristic signal that may distinguish it from other astrophysical sources., Comment: Movie: https://youtu.be/JE5FRG7kgvU Data: https://github.com/ThomasHelfer/BosonStarAfterglow

Although the paradigm of inflation has been extensively studied to demonstrate how macroscopic inhomogeneities in our universe originate from quantum fluctuations, most of the established literature ignores the crucial role that entanglement between the modes of the fluctuating field plays in its observable predictions. In this paper, we import techniques from quantum information theory to reveal hitherto undiscovered predictions for inflation which, in turn, signals how quantum entanglement across cosmological scales can affect large scale structure. Our key insight is that observable long-wavelength modes must be part of an open quantum system, so that the quantum fluctuations can decohere in the presence of an environment of short-wavelength modes. By assuming the simplest model of single-field inflation, and considering the leading order interaction term from the gravitational action, we derive a universal lower bound on the observable effect of such inescapable entanglement., Comment: 8 pages + 10 pages (Appendix); comments welcome

The standard interpretation of observations such as the peak apparent magnitude of Type Ia supernova made from one location in a lumpy Universe is based on the idealised Friedmann-Lema\^itre Robertson-Walker spacetime. All possible corrections to this model due to inhomogeneities are usually neglected. Here, we use the result from the recent concise derivation of the area distance in an inhomogeneous universe to study the monopole and Hubble residual of the apparent magnitude of Type Ia supernovae. We find that at low redshifts, the background FLRW spacetime model of the apparent magnitude receives corrections due to relative velocity perturbation in the observed redshift. We show how this velocity perturbation could contribute to a variance in the Hubble residual and how it could impact the calibration of the absolute magnitude of the Type Ia supernova in the Hubble flow. We also show that it could resolve the tension in the determination of the Hubble rate from the baryon acoustic oscillation and local measurements., Comment: Version accepted for publication by CQG

We thoroughly investigate conformally Schwarzschild spacetimes in different coordinate systems to seek for physically reasonable models of a cosmological black hole. We assume that a conformal factor depends only on the time coordinate and that the spacetime is asymptotically flat Friedmann-Lema\^{\i}tre-Robertson-Walker universe filled by a perfect fluid obeying a linear equation state $p=w\rho$ with $w>-1/3$. In this class of spacetimes, the McClure-Dyer spacetime, constructed in terms of the isotropic coordinates, and the Thakurta spacetime, constructed in terms of the standard Schwarzschild coordinates, are identical and do not describe a cosmological black hole. In contrast, the Sultana-Dyer and Culetu classes of spacetimes, constructed in terms of the Kerr-Schild and Painlev\'{e}-Gullstrand coordinates, respectively, describe a cosmological black hole. In the Sultana-Dyer case, the corresponding matter field in general relativity can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous null fluid, which is valid everywhere in the spacetime unlike Sultana and Dyer's interpretation. In the Culetu case, the matter field can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous anisotropic fluid. However, in both cases, the total energy-momentum tensor violates all the standard energy conditions at a finite value of the radial coordinate in late times. As a consequence, the Sultana-Dyer and Culetu black holes for $-1/3, Comment: 58 pages, 10 figures, 8 tables; v3, this version corrects the published version according to the corrigendum (2023 Class. Quantum Grav. 40, 079501). The main results remain unchanged

We heal the cosmological constant problem by means of a \emph{cancellation mechanism} that adopts a phase transition during which quantum fluctuations are eliminated. To this purpose, we propose that a generalized scalar (dark) matter field with a non-vanishing pressure term can remove the vacuum energy contribution, if its corresponding thermodynamics is written in terms of a \emph{quasi-quintessence} representation. In such a picture, pressure differs from quintessence as it shows a zero kinetic contribution. Using this field, we investigate a metastable transition phase, in which the universe naturally passes through an inflationary phase. To reach this target, we single out a double exponential potential, describing the metastable inflationary dynamics by considering suitable boundaries and thermodynamic conditions. We analyze stability investigating saddle, stable and unstable points and we thus predict a chaotic inflation that mimics the Starobinsky exponential potential. Consequently, the role of the proposed dark matter field is investigated throughout the overall universe evolution. To do so, we provide a physical explanation on unifying the dark sector with inflation by healing the cosmological constant problem., Comment: 13 pages, 3 figures, 2 tables

Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to be homogeneous and isotropic. Here we address the above questions in highly general cosmological models, with the only assumption being that the average flow of matter is irrotational. Using techniques from differential geometry, specifically extensions of the Bonnet-Myers theorem, we derive a condition which implies a finite universe and yields a bound for its diameter. Furthermore, under a weaker condition involving the interplay between curvature and diameter, together with the assumption that the universe is finite (i.e., has closed spatial slices), we provide a concise list of possible topologies. Namely, the spatial sections then would be either the ring topologies $S^1 \times S^2$, $S^1\tilde{\times}S^2$, $S^1\times\mathbb{RP}^2$, $\mathbb{RP}^3 \# \mathbb{RP}^3$, or covered by the sphere $S^3$ or torus $T^3$. In particular, under this condition the basic construction of connected sums would be ruled out (save for one), along with the plethora of topologies associated with negative curvature. These results are obtained from consequences of the geometrization of 3-manifolds, by applying a generalization of the almost splitting theorem together with a curvature formula of Ehlers and Ellis., 12 pages; final version

Constructing an extension of Newton's theory which is defined on a non-Euclidean topology (in the sense of Thurston's decomposition), called a non-Euclidean Newtonian theory, corresponding to the zeroth order of a non-relativistic limit of general relativity is an important step in the study of the backreaction problem in cosmology and might be a powerful tool to study the influence of global topology on structure formation. After giving a precise mathematical definition of such a theory, based on the concept of Galilean manifolds, we propose two such extensions, for spherical or hyperbolic topologies, using a minimal modification of the Newton-Cartan equations. However as for now we do not seek to justify this modification from general relativity. The first proposition features a non-zero cosmological backreaction, but the presence of gravitomagnetism and the impossibility of performing exact $N$-body calculations make this theory difficult to be interpreted as a Newtonian-like theory. The second proposition features no backreaction, exact $N$-body calculation is possible and no gravitomagnetism appears. In absence of a justification from general relativity, we argue that this non-Euclidean Newtonian theory should be the one to be considered, and could be used to study the influence of topology on structure formation via $N$-body simulations. For this purpose we give the mass point gravitational field in $\mathbb{S}^3$., Published in Classical and Quantum Gravity

We completely classify the Friedmann-Lema\^{i}tre-Robertson-Walker solutions with spatial curvature $K=0,\pm 1$ for perfect fluids with linear equation of state $p=w\rho $, where $\rho$ and $p$ are the energy density and pressure, without assuming any energy conditions. We extend our previous work to include all geodesics and parallelly propagated curvature singularities, showing that no non-null geodesic emanates from or terminates at the null portion of conformal infinity and that the initial singularity for $K=0,-1$ and $-5/3, Comment: 21 pages, 7 figures, major revision, published in Class. Quantum Grav

The total Hamiltonian in general relativity, which involves the first class Hamiltonian and momentum constraints, weakly vanishes. However, when the action is expanded around a classical solution as in the case of a single scalar field inflationary model, there appears a non-vanishing Hamiltonian and additional first class constraints; but this time the theory becomes perturbative in the number of fluctuation fields. We show that one can reorganize this expansion and solve the Hamiltonian constraint exactly, which yield an explicit all order action. On the other hand, the momentum constraint can be solved perturbatively in the tensor modes $\gamma_{ij}$ by still keeping the curvature perturbation $\zeta$ dependence exact. In this way, after gauge fixing, one can obtain a semi-exact Hamiltonian for $\zeta$ which only gets corrections from the interactions with the tensor modes (hence the Hamiltonian becomes exact when the tensor perturbations set to zero). The equations of motion clearly exhibit when the evolution of $\zeta$ involves a logarithmic time dependence, which is a subtle point that has been debated in the literature. We discuss the long wavelength and late time limits, and obtain some simple but non-trivial classical solutions of the $\zeta$ zero-mode., Comment: 19 pages, revtex 4-1, to appear in Classical and Quantum Gravity

We derive a theory-independent version of the momentum constraint equation for use in cosmology, as a part of the Parameterised Post-Newtonian Cosmology (PPNC) framework. Our equations are constructed by adapting the corresponding quantities from formalisms devised for testing and constraining gravity in isolated astrophysical systems, thereby extending the domain of applicability of these approaches up to cosmological scales. Our parameterised equations include both scalar and divergenceless-vector gravitational potentials, and can be applied to both conservative and non-conservative theories of gravity. They can also be used to describe the gravitational fields of both non-linear structures and super-horizon perturbations. We apply the parameterised equations we propose to quintessence models of dark energy, as well as to scalar-tensor and vector-tensor theories of gravity. We find them to work well in each case. Our equations are highly compact, and are intended to be useful for constraining gravity in a theory-independent fashion in cosmology., 26 pages, 2 figures, v2. Matches version published in CQG

The problem of radiation by the charged particles of the intergalactic medium (IGM) when a passing gravitational wave (GW) accelerate them is investigated. The largest acceleration (taking a charge from rest to a maximum speed which remains non-relativistic in the rest frame of the unperturbed spacetime) is found to be limited by the curvature of a propagating spherical gravitational wavefront. Interesting physics arises from the ensuing emission of radiation into the warm hot IGM, which to lowest order is a fully ionized hydrogen plasma with a frozen-in magnetic field $B$. It is found that for a vast majority of propagation directions, the right-handed polarized radiation can penetrate the plasma at frequencies below the plasma frequency $\om_p$, provided $\om, Comment: CQG in print

We consider the hypothesis that nonlocal, omnidirectional, causally-coherent quantum entanglement of inflationary horizons may account for some well-known measured anomalies of cosmic microwave background (CMB) anisotropy on large angular scales. It is shown that causal coherence can lead to less cosmic variance in the large-angle power spectrum C ℓ of primordial curvature perturbations on spherical horizons than predicted by the standard model of locality in effective field theory, and to new symmetries of the angular correlation function C(Θ). Causal considerations are used to construct an approximate analytic model for C(Θ) on angular scales larger than a few degrees. Allowing for uncertainties from the unmeasured intrinsic dipole and from Galactic foreground subtraction, causally-coherent constraints are shown to be consistent with measured CMB correlations on large angular scales. Reduced cosmic variance will enable powerful tests of the hypothesis with better foreground subtraction and higher fidelity measurements on large angular scales.

We study inflation as a "cosmic" renormalization-group flow. The flow, which encodes the dependence on the background metric, is described by a running coupling $\alpha $, which parametrizes the slow roll, a de Sitter free, analytic beta function and perturbation spectra that are RG invariant in the superhorizon limit. Using RG invariance as a guiding principle, we classify the main types of flows according to the properties of their spectra, without referring to their origins from specific actions or models. Novel features include spectra with essential singularities in $\alpha $ and violations of the relation $r+8n_{\text{t}}=0$ to the leading order. Various classes of potentials studied in the literature can be described by means of the RG approach, even when the action includes a Weyl-squared term, while others are left out. In known cases, the classification helps identify the models that are ruled out by data. The RG approach is also able to generate spectra that cannot be derived from standard Lagrangian formulations., Comment: 35 pages; v2: expanded intro with vocabulary RG flow cosmic RG flow, CQG

A gauge-invariant treatment of the monopole- ($l=0$) and dipole ($l=1$) modes in linear perturbations of the Schwarzschild background spacetime is proposed. Through this gauge-invariant treatment, we derived the solutions to the linearized Einstein equation for these modes with a generic matter field. In the vacuum case, these solutions include the Kerr parameter perturbations in the $l=1$ odd modes and the additional mass parameter perturbations of the Schwarzschild mass in the $l=0$ even modes. The linearized version of Birkhoff's theorem is also confirmed in a gauge-invariant manner. In this sense, our proposal is reasonable., (v1) 10 pages, no figure; (v2) 16 pages, Section 2 is added for the explanation of our previous works, Additional explanations are added, references are added and re-organized; (v3) Some explanations are added, Typos are corrected

Intensity maps of the 21cm emission line of neutral hydrogen are lensed by intervening large-scale structure, similar to the lensing of the cosmic microwave background temperature map. We extend previous work by calculating the lensing contribution to the full-sky 21cm bispectrum in redshift space. The lensing contribution tends to peak when equal-redshift fluctuations are lensed by a lower redshift fluctuation. At high redshift, lensing effects can become comparable to the contributions from density and redshift-space distortions., Comment: 8 pages + 2 appendices + references. Version accepted by Class. Quant. Grav

In this paper we attempt to answer to the question: can cosmic acceleration of the Universe have a fractal solution? We give an exact solution of a Lema\^itre-Tolman-Bondi (LTB) Universe based on the assumption that such a smooth metric is able to describe, on average, a fractal distribution of matter. While the LTB model has a center, we speculate that, when the fractal dimension is not very different from the space dimension, this metric applies to any point of the fractal structure when chosen as center so that, on average, there is not any special point or direction. We examine the observed magnitude-redshift relation of type Ia supernovae (SNe Ia), showing that the apparent acceleration of the cosmic expansion can be explained as a consequence of the fractal distribution of matter when the corresponding space-time metric is modeled as a smooth LTB one and if the fractal dimension on scales of a few hundreds Mpc is $D=2.9 \pm 0.02$., Comment: 6 pages, 4 figures, accepted for publication in Classical and Quantum Gravity

We study the extent up to which the equivalence principle is obeyed in models of modified gravity and dark energy involving a single scalar degree of freedom. We focus on the effective field theories of dark energy describing the late time acceleration in the presence of ordinary matter species. In their covariant form these coincide with the Horndeski theories on a cosmological background with a slowly varying Hubble rate and a time-dependent scalar field. We show that in the case of an exactly de Sitter universe both the weak and strong equivalence principles hold. This occurs due to the combination of the shift symmetry of the scalar and the time translational invariance of de Sitter space. When generalized to Friedmann--Robertson--Walker cosmologies (FRW) we show that the weak equivalence principle is obeyed for test particles and extended objects in the quasi-static subhorizon limit. We do this by studying the field created by an extended object moving in an FRW background as well as its equation of motion in an external gravitational field. We also estimate the corrections to the geodesic equation of the extended object due to the approximations made., Comment: 22 pages

Quasilocal definitions of stress-energy-momentum -- that is, in the form of boundary densities (rather than local volume densities) -- have proven generally very useful in formulating and applying conservation laws in general relativity. In this paper, we present a detailed application of such definitions to cosmology, specifically using the Brown-York quasilocal stress-energy-momentum tensor for matter and gravity combined. We compute this tensor, focusing on the energy and its associated conservation law, for FLRW spacetimes with no pertubrations and with scalar cosmological perturbations. For unperturbed FLRW spacetimes, we emphasize the importance of the vacuum energy (for both flat and curved space), which is almost universally underappreciated (and usually "subtracted"), and discuss the quasilocal interpretation of the cosmological constant. For the perturbed FLRW spacetime, we show how our results recover or relate to the more typical effective local treatment of energy in cosmology, with a view towards better studying the issues of the cosmological constant and of cosmological back-reactions., Comment: v1: 28 pages, 3 figures; v2: 30 pages. References and comments added; v3: 35 pages. New subsection (IV A) added

We propose that several of the anomalies that have been observed at large angular scales in the CMB have a common origin in a cosmic bounce that took place before the inflationary era. The bounce introduces a new physical scale in the problem, which breaks the almost scale invariance of inflation. As a result, the state of scalar perturbations at the onset of inflation is no longer the Bunch-Davies vacuum, but it rather contains excitations and non-Gaussianity, which are larger for infrared modes. We argue that the combined effect of these excitations and the correlations between CMB modes and longer wavelength perturbations, can account for the observed power suppression, for the dipolar asymmetry, and it can also produce a preference for odd-parity correlations. The model can also alleviate the tension in the lensing amplitude $A_L$. We adopt a phenomenological viewpoint by characterizing the model with a few free parameters, rather than restricting to specific bouncing theories. We identify the minimum set of ingredients needed for our ideas to hold, and point out examples of theories in the literature where these conditions are met., 45 pages, 16 figures, 6 tables

In this paper, we consider dynamical Chern-Simons gravity with the identification of the scalar field coupled though the Pontryagin density with the axion dark matter, and we discuss the effects of the parametric resonance on gravitational waves (GWs). When we consider GWs in a coherently oscillating axion cloud, we confirm that significant resonant amplification of GWs occurs in a narrow frequency band, and the amplification is restricted to the late epoch after the passage of the incident waves. We also identify the condition that an axion cloud spontaneously emits GWs. Once we take into account the randomness of the spatial phase distribution of the axion oscillations, we find that the amplification is suppressed compared with the coherent case, but significant amplification of GWs can still occur. We also examine whether or not the amplification of GWs is possible in the present universe, taking into account the history of the universe. We find that resonant amplification is difficult to be tested from GW observations in the standard scenario of the axion DM model, in which the axion is the dominant component of DM. However, there is some parameter window in which the resonant amplification of GWs might be observed, if the axion is subdominant component of DM, and the axion cloud formation is delayed until the Hubble rate becomes much smaller than the axion mass., 26 pages, 7 figures

We examine a novel class of toy models of cosmological inhomogeneities by smoothly matching along a suitable hypersurface an arbitrary number of sections of "quasi flat" inhomogeous and anisotropic Szekeres-II models to sections of any spatially flat cosmology that can be described by the Robertson-Waker metric (including de Sitter, anti de Sitter and Minkowski spacetimes). The resulting "pancake" models are quasi-flat analogues to the well known spherical "Swiss-cheese" models found in the literature. Since Szekeres-II models can be, in general, compatible with a wide range of sources (dissipative fluids, mixtures of non-comoving fluids, mixtures of fluids with scalar or magnetic fields or gravitational waves), the pancake configurations we present allow for a description of a wide collection of localized sources embedded in a Robertson-Waker geometry. We provide various simple examples of arbitrary numbers of Szekeres-II regions (whose sources are comoving dust and energy flux interpreted as a field of peculiar velocities) matched with Einstein de Sitter, $\Lambda$CDM and de Sitter backgrounds. We also prove that the Szekeres-II regions can be rigorously regarded as "exact" perturbations on a background defined by the matching discussed above. We believe that these models can be useful to test ideas on averaging and backreaction and on the effect of inhomogeneities on cosmic evolution and observations., Comment: 19 pages, 4 figures

We study evolution of perturbations in dark matter and dark energy for spherical collapse. We study Tachyon models of dark energy using the approach outlined in Rajvanshi and Bagla (2018). We work with models that are allowed by current observations. We find that as with Quintessence models allowed by observations, dark energy perturbations do not affect evolution of perturbations in dark matter in a significant manner. Perturbations in dark energy remain small for such models. In order to compare different classes of dark energy models, we use reconstruction of potentials and study dark matter and dark energy perturbations for same expansion history in the two models. We find that dark matter perturbations carry no imprint of the class of dark energy models for the same expansion history: this is significant in that we can work with any convenient model to study clustering of dark matter. We find that the evolution of dark energy perturbations carries an imprint of the class of models in that these grow differently in Tachyon models and Quintessence models. However, the difference between these diminishes for (1+w)<, 18 Pages, final (accepted) version

The primordial stochastic gravitational wave background (SGWB) carries first-hand messages of early-universe physics, possibly including effects from inflation, preheating, cosmic strings, electroweak symmetry breaking, and etc. However, the astrophysical foreground from compact binaries may mask the SGWB, introducing difficulties in detecting the signal and measuring it accurately. In this paper, we propose a foreground cleaning method taking advantage of gravitational wave observations in other frequency bands. We apply this method to probing the SGWB with space-borne gravitational wave detectors, such as the laser interferometer space antenna (LISA). We find that the spectral density of the LISA-band astrophysical foreground from compact binaries (black holes and neutron stars) can be predicted with percent-level accuracy assuming 10-years’ observations of third-generation GW detectors, e.g., cosmic explorer. While this multi-band method does not apply to binary white dwarfs (BWDs) which usually merger before entering the frequency band of ground-based detectors, we limit our foreground cleaning to frequency higher than ∼5 mHz, where all galactic BWDs can be individually resolved by LISA and the shape of the spectral density of the foreground from extragalactic BWDs can be reconstructed and/or modeled with certain uncertainties. After the foreground cleaning, LISA’s sensitivity to the primordial SGWB will be substantially improved for either two LISA constellations where SGWB can be measured by cross correlating their outputs or only one constellation with three spacecrafts where SGWB can be measured by contrasting the responses of a signal channel and a null channel.

We perform a detailed analysis for the dynamics of Chiral cosmology in a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker universe with a mixed potential term. The stationary points are categorized in four families. Previous results in the literature are recovered while new phases in the cosmological evolution are found. From our analysis we find nine different cosmological solutions, the eight describe scaling solutions, where the one is that of a pressureless fluid, while only one de Sitter solution is recovered., Comment: 20 pages, 10 figures, 1 table, version accepted for publication in Classical and Quantum Gravity

In the recent years, the field of fast radio bursts (FRBs) is thriving and growing rapidly. It is of interest to study cosmology by using FRBs with known redshifts. In the present work, we try to test the possible cosmic anisotropy with the simulated FRBs. In particular, we only consider the possible dipole in FRBs, rather than the cosmic anisotropy in general, while the analysis is only concerned with finding the rough number of necessary data points to distinguish a dipole from a monopole structure through simulations. Noting that there is no a large sample of actual data of FRBs with known redshifts by now, simulations are necessary to this end. We find that at least 2800, 190, 100 FRBs are competent to find the cosmic dipole with amplitude 0.01, 0.03, 0.05, respectively. Unfortunately, even 10000 FRBs are not competent to find the tiny cosmic dipole with amplitude of ${\cal O}(10^{-3})$. On the other hand, at least 20 FRBs with known redshifts are competent to find the cosmic dipole with amplitude 0.1. We expect that such a big cosmic dipole could be ruled out by using only a few tens of FRBs with known redshifts in the near future., 16 pages, 6 figures, revtex4; v2: discussions added, Class. Quant. Grav. in press; v3: published version

We extend various recent results regarding the derivation of effective cosmological Friedmann equations from the dynamics of group field theory (GFT). Restricting ourselves to a single GFT field mode (or fixed values of Peter-Weyl representation labels), we first consider dynamics given by a quadratic Hamiltonian, which takes the form of a squeezing operator, and then add a quartic interaction that can be seen as a toy model for interactions in full GFT. Our derivation of effective Friedmann equations does not require a mean-field approximation; we mostly follow a general approach in which these equations in fact hold for any state. The resulting cosmological equations exhibit corrections to classical Friedmann dynamics similar to those of loop quantum cosmology, leading to generic singularity resolution, but also involve further state-dependent terms. We then specify these equations to various types of coherent states, such as Fock coherent states or Perelomov-Gilmore states based on the su(1,1) structure of harmonic quantum cosmology. We compute relative uncertainties of volume and energy in these states, clarifying whether they can be interpreted as semiclassical. In the interacting case, both analytical and numerical approximations are used to obtain modified cosmological dynamics. Our results clarify how effective cosmological equations derived from GFT can provide reliable approximations to the full dynamics., 38 pages, 5 figures; v2: improved discussion, added references, additional figure

We formulate and solve the problem of Newtonian cosmology under the assumption that the absolute space of Newton is non-Euclidean. In particular, we focus on the negatively-curved hyperbolic space, H3. We point out the inequivalence between the curvature term that arises in the Friedmann equation in Newtonian cosmology in Euclidean space and the role of curvature in the H3 space. We find the generalisation of the inverse-square law and the solutions of the Newtonian cosmology that follow from it. We find the generalisations of the Euclidean Michell 'black hole' in H3 and show that it leads to different maximum force and area results to those we have found in general relativity. We show how to add the counterpart of the cosmological constant to the gravitational potential in H3 and explore the solutions and asymptotes of the cosmological models that result. We also discuss the problems of introducing compact topologies in Newtonian cosmologies with non-negative spatial curvature., Comment: 11 pages, no figures

The odd parity gravitational Quasi-Normal Mode spectrum of black holes with non-trivial scalar hair in Horndeski gravity is investigated. We study `almost' Schwarzschild black holes such that any modifications to the spacetime geometry (including the scalar field profile) are treated as small quantities. A modified Regge-Wheeler style equation for the odd parity gravitational degree of freedom is presented to quadratic order in the scalar hair and spacetime modifications, and a parameterisation of the modified Quasi-Normal Mode spectrum is calculated. In addition, statistical error estimates for the new hairy parameters of the black hole and scalar field are given., Updated to match Classical and Quantum Gravity accepted version

Recently, Tsupko et al. have put forward the very interesting proposal to use the shadows of high-redshift supermassive black holes (SMBHs) as standard rulers. This would in principle allow us to probe the expansion history within a redshift range which would otherwise be challenging to access. In this note, we critically examine this proposal, and identify a number of important issues which had been previously overlooked. These include difficulties in obtaining reliable SMBH mass estimates and reaching the required angular resolution, and an insufficient knowledge of the accretion dynamics of high-redshift SMBHs. While these issues currently appear to prevent high-redshift SMBH shadows from being used as robust standard rulers, we hope that our flagging them early will help in making this probe theoretically mature by the time it will be experimentally feasible., 12 pages, 1 figure. Added references and improved discussion on weak lensing. Version accepted for publication in Class. Quant. Grav

The ADM formalism together with a constant mean curvature (CMC) temporal gauge is used to derive the monotonic decay of a weak Lyapunov function of the Einstein dynamical equations in an expanding universe with a positive cosmological constant and matter sources satisfying suitable energy conditions. While such a Lyapunov function does not, in general, represent a true Hamiltonian of the matter-coupled gravity dynamics (unlike in the vacuum case when it does), it can nevertheless be used to study the asymptotic behavior of the spacetimes. The Lyapunov function attains its infimum only in the limit that the matter sources be `turned off` or, at least, become asymptotically negligible provided that the universe model does not re-collapse and form singularities. Later we specialize our result to the case of a perfect fluid which satisfies the desired energy conditions. However, even in this special case, we show using Shutz's velocity potential formalism cast into Hamiltonian form that unlike the vacuum spacetimes (with or without a positive cosmological constant), construction of a true Hamiltonian for the dynamics in constant mean curvature temporal gauge is difficult and therefore the Lyapunov function does not have a straightforward physical interpretation. Nevertheless, we show, for the fluid with equation of state $P=(\gamma-1)\rho$ ($1\leq\gamma\leq2$), that the general results obtained hold true and the infimum of the weak Lyapunov function can be related to the Sigma constant, a topological invariant of the manifold. Utilizing these results, some general conclusions are drawn regarding the asymptotic state of the universe and the dynamical control of the allowed spatial topologies in the cosmological models.

The well-noted correspondence between gravitation and electrodynamics emphasizes the importance of the Lanczos tensor -- the potential of the Weyl tensor -- which is an inherent structural element of any metric theory of gravity formulated in a 4-dimensional pseudo Riemannian spacetime. However, this ingenious discovery has gone largely unnoticed. We elucidate this important quantity by deriving its expressions in some particularly chosen spacetimes and try to find out what it represents actually. We find out that the Lanczos potential tensor does not represent the potential of the gravitational field, as is ascertained by various evidences. Rather, it is enriched with various signatures of quantum character, which provides a novel insight into the heart of a geometric embodiment of gravity., Comment: Published in CQG

We show, through an explicit calculation of the relevant Green's functions, that the transverse-traceless (TT) portion of the gravitational perturbations of Minkowski spacetime and of spatially flat cosmologies with a constant equation-of-state $w$ receive contributions from their isolated matter source(s) outside the past null cone of the observer. This implies the TT gravitational wave (GW) cannot be a standalone observable -- despite widespread (apparent) claims in the gravitational wave literature to the contrary. About a Minkowski background, all 4 of the gauge-invariant variables -- the two scalars, one vector and tensor -- play crucial roles to ensure the spatial tidal forces encoded within the gauge-invariant linearized Riemann tensor are causal. These gravitational tidal forces do not depend solely on the TT graviton but rather on the causal portion of its acceleration. However, in the far zone radiative limit, the flat spacetime `TT' graviton Green's function does reduce to the causal `tt' ones, which are the ones commonly used to compute gravitational waveforms. Similar remarks apply to the spin-1 photon; for instance, the electric field does not depend solely on the photon, but is the causal part of its velocity. As is known within the quantum theory of photons and linearized gravitons, there are obstacles to the construction of simultaneously gauge-invariant and Lorentz-covariant descriptions of these massless spin-1 and spin-2 states. Our results transparently demonstrate that the quantum operators associated with the helicity-1 photon and helicity-2 linear graviton both violate micro-causality: namely, they do not commute outside the light cone in flat and cosmological spacetimes., v3: 64 pages, 1 figure, 4D Minkowski results summarized in Sec. VI, version accepted by CQG. v4: Minor corrections made

Recently, Kenna-Allison et.al. claimed that bimetric gravity cannot give rise to a viable cosmological expansion history while at the same time being compatible with local gravity tests. In this note we review that claim and combine various results from the literature to provide several simple counter examples. We conclude that the results of Kenna-Allison et.al. cannot hold in general., 6 pages, 2 figures

In this paper we consider a model based on interacting $p-$forms and explore some cosmological applications. Restricting to gauge invariant actions, we build a general Lagrangian allowing for arbitrary interactions between the $p-$forms (including interactions with a $0-$form, scalar field) in a given background in $D$ dimensions. For simplicity, we restrict the construction to up to first order derivatives of the fields in the Lagrangian. We discuss with detail the four dimensional case and devote some attention to the mechanism of topological mass generation originated by couplings of the form $B\wedge F$ between a $p-$form and a $(3-p)-$form. As a result, we show the system of the interacting $p-$forms $(p=1,2,3)$ is equivalent to a parity violating, massive, Proca vector field model. Finally, we discuss some cosmological applications. In a first case we study a very minimalistic system composed by a $3-$form coupled to a $0-$form. The $3-$form induces an effective potential which acts as a cosmological constant term suitable to drive the late time accelerated expansion of the universe dominated by dark energy. We study the dynamics of the system and determine its critical points and stability. Additionally, we study a system composed by a scalar field and a $1$-form. This case is interesting because the presence of a coupled $1-$form can generate non vanishing anisotropic signatures during the late time accelerated expansion. We discuss the evolution of cosmological parameters such as the equation of state in this model., Comment: Several modifications and updates. The discussion about the $3-$forms is reviewed and corrected. A new application included. Several references added. Main conclusions unchanged

We review current theoretical cosmology, including fundamental and mathematical cosmology and physical cosmology (as well as cosmology in the quantum realm), with an emphasis on open questions., Some references updated. Published as Topical Review in CQG

We show how Conformal Gravity (CG) has to satisfy a fine-tuning condition to describe the rotation curves of disk galaxies without the aid of dark matter. Interpreting CG as a gauge natural theory yields conservation laws and their associated superpotentials without ambiguities. We consider the light deflection of a point-like lens and impose that the two Schwarzschild-like metrics with and without the lens are identical at infinite distances from the lens. The energy conservation law implies that the parameter $\gamma$ in the linear term of the metric has to vanish, otherwise the two metrics are physically inaccessible from each other. This linear term is responsible to mimic the role of dark matter in disk galaxies and gravitational lensing systems. Our analysis shows that removing the need of dark matter with CG thus relies on a fine-tuning condition on $\gamma$. We also illustrate why the results of previous investigations of gravitational lensing in CG largely disagree. These discrepancies derive from the erroneous use of the deflection angle definition adopted in General Relativity, where the vacuum solution is asymptotically flat, unlike CG. In addition, the lens mass is identified with various combinations of the metric parameters. However, these identifications are arbitrary, because the mass is not a conformally invariant quantity, unlike the conserved charge associated to the energy conservation law. Based on this conservation law and by removing the fine-tuning condition on $\gamma$, i.e. by setting $\gamma=0$, the energy difference between the metric with the point-like lens and the metric without it defines a conformally invariant quantity that can in principle be used for (1) a proper derivation of light deflection in CG, and (2) the identification of the lens mass with a function of the parameters $\beta$ and $k$ of the Schwarzschild-like metric., Comment: 16 pages, 1 figure. Revised version according to the referees comments. The results reported in the original version remain unchanged

We examine the implementation of Buchert's and Green & Wald's averaging formalisms in exact spherically symmetric and plane symmetric dust-filled cosmological models. We find that, given a cosmological space-time, Buchert's averaging scheme gives a faithful way of interpreting the large-scale expansion of space, and explicit terms that precisely quantify deviations from the behaviour expected from the Friedmann equations of homogeneous and isotropic cosmological models. The Green & Wald formalism, on the other hand, does not appear to yield any information about the large-scale properties of a given inhomogeneous space-time. Instead, this formalism is designed to calculate the back-reaction effects of short-wavelength fluctuations around a given "background" geometry. We find that the inferred expansion of space in this approach is entirely dependent on the choice of this background, which is not uniquely specified for any given inhomogeneous space-time, and that the "back-reaction" from small-scale structures vanishes in every case we study. This would appear to limit the applicability of Green & Wald's formalism to the study of large-scale expansion in the real Universe, which also has no pre-defined background. Further study is required to enhance the evaluation and comparison of these averaging formalisms, and determine whether the same difficulties exist, in less idealized space-time geometries., 34 pages, 7 figures

We consider single-field inflation in light of string-motivated "swampland" conjectures suggesting that effective scalar field theories with a consistent UV completion must have field excursion $\Delta \phi \lesssim M_{\rm Pl}$, in combination with a sufficiently steep potential, $M_{\rm Pl} V_\phi/V \gtrsim {\cal O}(1)$. Here, we show that the swampland conjectures are inconsistent with existing observational constraints on single-field inflation. Focusing on the observationally favoured class of concave potentials, we map the allowed swampland region onto the $n_S$-$r$ "zoo plot" of inflationary models, and find that consistency with the Planck satellite and BICEP2/Keck Array requires $M_{\rm Pl} V_\phi/V \lesssim 0.1$ and $-0.02 \lesssim M_{\rm Pl}^2 V_{\phi\phi}/V < 0$, in strong tension with swampland conjectures. Extension to non-canonical models such as DBI Inflation does not significantly weaken the bound., Comment: 5 pages, 1 figure. The busy reader should skip directly to Fig. 1, where the swampland-allowed region is mapped onto the $n_S$-$r$ plane. v2: added discussion on the refined swampland conjecture, basic conclusions unchanged. v3: version accepted for publication in Class. Quant. Grav

Binary black hole mergers are of great interest to the astrophysics community, not least because of their promise to test general relativity in the highly dynamic, strong field regime. Detections of gravitational waves from these sources by LIGO and Virgo have garnered widespread media and public attention. Among these sources, precessing systems (with misaligned black-hole spin/orbital angular momentum) are of particular interest because of the rich dynamics they offer. However, these systems are, in turn, more complex compared to nonprecessing systems, making them harder to model or develop intuition about. Visualizations of numerical simulations of precessing systems provide a means to understand and gain insights about these systems. However, since these simulations are very expensive, they can only be performed at a small number of points in parameter space. We present binaryBHexp, a tool that makes use of surrogate models of numerical simulations to generate on-the-fly interactive visualizations of precessing binary black holes. These visualizations can be generated in a few seconds, and at any point in the 7-dimensional parameter space of the underlying surrogate models. With illustrative examples, we demonstrate how this tool can be used to learn about precessing binary black hole systems., Comment: Matches CQG version. Visualizations available at https://vijayvarma392.github.io/binaryBHexp

In this paper we study the effects of spatial curvature of the metric on the phase space of vacuum $f(R)$ gravity. Particularly, we appropriately choose the variables of the dynamical system, in order for this to be autonomous, and we study the phase space of the resulting theory, focusing on de Sitter, matter and radiation domination fixed points. Our analysis indicates that the effect of spatial curvature on the phase space is radical, since it destabilizes all the stable de Sitter vacua of the flat spacetime vacuum $f(R)$ gravity phase space, making the phase space having non-trivial unstable submanifolds. This instability occurs regardless if the spacetime has elliptic or hyperbolic spatial sections, and it is also robust towards the choice of initial conditions. We investigate the source of the instability in the system, and also we discuss the stability of the matter and radiation domination vacua, which, as we demonstrate, are also highly unstable. Our results for de Sitter attractors indicate that the stable de Sitter attractors of the vacuum $f(R)$ gravity theory for a flat Universe, are destabilized by the presence of curvature, and this shows that inflation for vacuum $f(R)$ gravity in non-flat spacetime is problematic, at least at the phase space level. This result holds true for both elliptic and hyperbolic spacetimes., CQG Accepted

We study possibilities to explain the whole dark matter abundance by primordial black holes (PBHs) or to explain the merger rate of binary black holes estimated from the gravitational wave detections by LIGO/Virgo. We assume that the PBHs are originated in a radiation- or matter-dominated era from large primordial curvature perturbation generated by inflation. We take a simple model-independent approach considering inflation with large running spectral indices which are parametrized by $n_\text{s}, \alpha_\text{s}$, and $\beta_\text{s}$ consistent with the observational bounds. The merger rate is fitted by PBHs with masses of $\mathcal{O}(10)$ $M_{\odot}$ produced in the radiation-dominated era. Then the running of running should be $\beta_\text{s} \sim 0.025$, which can be tested by future observation. On the other hand, the whole abundance of dark matter is consistent with PBHs with masses of asteroids ($\mathcal{O}(10^{-17})~M_{\odot}$) produced in an early matter-dominated era if a set of running parameters are properly realized., Comment: 27 pages, 7 figures; Figures are replaced with the correct ones. (In v3, older versions of figures were accidentally uploaded.)

It is shown that a spontaneously-broken gauge theory of the Lorentz group contains Ashtekar's chiral formulation of General Relativity accompanied by dust. From this perspective, gravity is described entirely by a connection $\omega$ valued in the Lie algebra of the complexified Lorentz group and a Lorentz-charged scalar field $\tau$. The model is "pre-geometric" in the sense that the spacetime metric may be constructed only in the symmetry-broken regime. We speculate on the extent to which this dust may account for dark matter and on the behaviour of the theory in regimes where the symmetry is not broken., Comment: v2 with minor edits, as published

We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ counterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop. A number of identities are derived which should facilitate further graviton loop computations., Comment: 61 pages, 1 figure, 11 tables, version 2 (63 pages) revised for publication in CQG

Extendibility of inflationary spacetimes with flat spatial geometry is investigated. We find that the past boundary of an inflationary spacetime becomes a so-called parallely propagated curvature singularity if the ratio $\dot{H}/a^2$ diverges at the boundary, where $\dot{H}$ and $a$ represent the time derivative of the Hubble parameter and the scale factor, respectively. On the other hand, if the ratio $\dot{H}/a^2$ converges, then the past boundary is regular and continuously extendible. We also develop a method to judge the continuous ($C^0$)extendibility of spacetime in the case of slow-roll inflation driven by a canonical scalar field. As applications of this method, we find that Starobinsky inflation has a $C^0$ parallely propagated curvature singularity, but a small field inflation model with a Higgs-like potential does not. We also find that an inflationary solution in a modified gravity theory with limited curvature invariants is free of such a singularity and is smoothly extendible., Comment: 14 pages, 4 figures, published version

We study the linear evolution of magnetised cosmological perturbations in the post-recombination epoch. Using full general relativity and adopting the ideal magnetohydrodynamic approximation, we refine and extend the previous treatments. More specifically, this is the first relativistic study that accounts for the effects of the magnetic tension, in addition to those of the field's pressure. Our solutions show that on sufficiently large scales, larger than the (purely magnetic) Jeans length, the perturbations evolve essentially unaffected by the magnetic presence. The magnetic pressure dominates on small scales, where it forces the perturbations to oscillate and decay. Close to the Jeans length, however, the field's tension takes over and leads to a weak growth of the inhomogeneities. These solutions clearly demonstrate the opposing action of the aforementioned two magnetic agents, namely of the field's pressure and tension, on the linear evolution of cosmological density perturbations., Invited contribution to the CQG Focus special issue "Magnetic fields at cosmological scales". Published version

We completely classify Friedmann-Lema\^{i}tre-Robertson-Walker solutions with spatial curvature $K=0,\pm 1$ and equation of state $p=w\rho$, according to their conformal structure, singularities and trapping horizons. We do not assume any energy conditions and allow $\rho < 0$, thereby going beyond the usual well-known solutions. For each spatial curvature, there is an initial spacelike big-bang singularity for $w>-1/3$ and $\rho>0$, while no big-bang singularity for $w0$. For $K=0$ or $-1$, $-10$, there is an initial null big-bang singularity. For each spatial curvature, there is a final spacelike future big-rip singularity for $w0$, with null geodesics being future complete for $-5/3\le w-1/3$, the universe contracts from infinity, then bounces and expands to infinity; for $-1, Comment: 37 pages, 8 figures, minor correction, accepted for publication in Classical and Quantum Gravity

In this paper we consider the Dvali and G\'omez assumption that the end state of a gravitational collapse is a Bose-Einstein condensate of gravitons. We then construct the two Gross-Pitaevskii equations for a static and spherically symmetric configuration of the condensate. These two equations correspond to the constrained minimisation of the gravitational Hamiltonian with respect to the redshift and the Newtonian potential, per given number of gravitons. We find that the effective geometry of the condensate is the one of a gravastar (a DeSitter star) with a sub-Planckian cosmological constant, for masses larger than the Planck scale. Thus, a condensate corresponding to a semiclassical black hole, is always quantum and weakly coupled. Finally, we obtain that the boundary of our gravastar, although it is not the location of a horizon, corresponds to the Schwarzschild radius., Comment: v.4: Accepted for publication. 10 pages

In this paper we investigate the so called "phantom barrier crossing" issue in a cosmological model based in the scalar-tensor theory with non-minimal derivative coupling to the Einstein's tensor. Special attention will be paid to the physical bounds on the squared sound speed. The numeric results are geometrically illustrated by means of a qualitative procedure of analysis that is based on the mapping of the orbits in the phase plane onto the surfaces that represent physical quantities in the extended phase space, that is: the phase plane complemented with an additional dimension relative to the given physical parameter. We find that the cosmological model based in the non-minimal derivative coupling theory -- this includes both the quintessence and the pure derivative coupling cases -- has serious causality problems related with superluminal propagation of the scalar and tensor perturbations. Even more disturbing is the finding that, despite that the underlying theory is free of the Ostrogradsky instability, the corresponding cosmological model is plagued by the Laplacian (classical) instability related with negative squared sound speed. This instability leads to an uncontrollable growth of the energy density of the perturbations that is inversely proportional to their wavelength. We show that independent of the self-interaction potential, for the positive coupling the tensor perturbations propagate superluminally, while for the negative coupling a Laplacian instability arises. This latter instability invalidates the possibility for the model to describe the primordial inflation., 26 pages, 27 eps figures. Version accepted by the CQG journal

We investigate the realization of the emergent universe scenario in theories with natural UV cutoffs, namely a minimum length and a maximum momentum, quantified by a new deformation parameter in the generalized uncertainty principle. We extract the Einstein static universe solutions and we examine their stability through a phase-space analysis. As we show, the role of the new deformation parameter is crucial in a twofold way: Firstly, it leads to the appearance of new Einstein static universe critical points, that are absent in standard cosmology. Secondly, it provides a way for a graceful exit from the Einstein static universe into the expanding thermal history, that is needed for a complete and successful realization of the emergent universe scenario., 9 pages, 5 figures, version published in Class.Quant.Grav