Search

Modified Newtonian Dynamics (MOND) has long been known to fail in galaxy clusters, implying a residual missing mass problem for clusters in this context. Here, using mass profiles derived from strong- and weak-lensing shear, as well as magnification data, for a sample of clusters from the CLASH survey, we characterize the density profile of this residual MOND missing mass in the central Mpc of galaxy clusters. In line with results obtained in the literature from the hydrostatic equilibrium of hot gas, we find that an inner constant density core and an outer power-law slope between $-4$ and $-6$ provides a good description within $\sim 1$ Mpc. We also show that the data in the central parts of clusters can be even better represented by a `dark mass-follows-gas' profile with an exponential cut-off. Clusters with X-ray emitting gas masses $M_\text{gas} \geq 10^{14}\, {\rm M}_\odot$ display a remarkable uniformity for the missing-to-hot-gas density ratio in the inner parts, of order $\sim$10, and for the exponential cut-off radius, of order $\sim 450$ kpc. Clusters with lower observed gas mass display larger and more scattered values for both the density ratio and cut-off radius. These lensing results can in principle serve as a crucible for relativistic theories of MOND in galaxy clusters, or for any other tentative hypothesis regarding the nature of the clusters residual missing mass in the MOND context., Comment: 12 pages, 4 figures

We revisit multi-messenger constraints from neutron star mergers on the speed of propagation of gravitational and electromagnetic waves in Horndeski and beyond Horndeski theories. By considering non-trivial couplings between the dark energy field and the electromagnetic sector, the electromagnetic wave can propagate through the cosmological background at non-unit speed, altering the phenomenological constraints on its gravitational counterpart. In particular, we show that recent models derived from a Kaluza-Klein compactification of higher dimensional Horndeski models fall into a broader class of theories disformally related to those whose gravitational waves propagate with unit speed. This disformal equivalence can, however, be broken by the gravitational couplings to other sectors with interesting phenomenological consequences. We also consider higher order couplings between the scalar and the photon with second order field equations, and show that they are not compatible with constraints coming from multi-messenger speed tests and the decay of the gravitational wave., Comment: 7 pages plus references

We present a pipeline to infer the equation of state of neutron stars from observations based on deep neural networks. In particular, using the standard (deterministic), as well as Bayesian (probabilistic) deep networks, we explore how one can infer the interior speed of sound of the star given a set of mock observations of total stellar mass, stellar radius and tidal deformability. We discuss in detail the construction of our simulated dataset of stellar observables starting from the solution of the gravitational equations, as well as the relevant architectures for the deep networks, along with their performance and accuracy. We further explain how our pipeline is capable to detect a possible QCD phase transition in the stellar core. Our results show that deep networks offer a promising tool towards solving the inverse problem of neutron stars, and the accurate inference of their interior from future stellar observations., Comment: 15 pages, 11 figures, code and supplementary material available at https://zenodo.org/records/11216586

Chaos is an intriguing phenomenon that can be found in an immense variate of systems. Its detection and discrimination from its counterpart order poses an interesting challenge. To address it, we present a deep classifier capable of classifying chaos from order in the discretised dynamics of Hamiltonian systems of two degrees of freedom, through the machinery of Poincar\'{e} maps. Our deep network is based predominantly on a convolutional architecture, and generalises with good accuracy on unseen datasets, thanks to the universal features of a perturbed pendulum learned by the deep network. We discuss in detail the significance and the preparation of our training set, and we showcase how our deep network can be applied to the dynamics of geodesic motion in an axi-symmetric and stationary spacetime of a compact object deviating from the Kerr black hole paradigm. Finally, we discuss current challenges and some promising future directions., Comment: 11 pages, 5 figures

We describe a simple and efficient Python code to perform Bayesian forecasting for gravitational waves (GW) produced by Extreme-Mass-Ratio-Inspiral systems (EMRIs). The code runs on GPUs for an efficient parallelised computation of thousands of waveforms and sampling of the posterior through a Markov-Chain-Monte-Carlo (MCMC) algorithm. EMRI_MC generates EMRI waveforms based on the so--called kludge scheme, and propagates it to the observer accounting for cosmological effects in the observed waveform due to modified gravity/dark energy. The code provides a helpful resource for forecasts for interferometry missions in the milli-Hz scale, e.g the satellite-mission LISA., Comment: v2: version to appear on SciPost Physics Codebases, code improved available at https://doi.org/10.5281/zenodo.10204186; v1: 14 pages, 2 figures

It has been hypothesized that dark matter is comprised of ultra-light bosons whose collective phenomena can be described as a scalar field undergoing coherent oscillations. Examples include axion and fuzzy dark matter models. In this ultra-light dark matter scenario, the harmonic variation in the field's energy-momentum tensor sources an oscillating component of the gravitational potential that we show can resonantly-excite stellar oscillations. A mathematical framework for predicting the amplitude of these oscillations is developed, which reveals that ultra-light dark matter predominantly excites p-modes of degree $l=1$. An investigation of resonantly-excited solar oscillations is presented, from which we conclude that dark matter-induced oscillations of the Sun are likely undetectable. We discuss prospects for constraining ultra-light dark matter using other stellar objects., Comment: 5 pages, no figures. Comments welcome. A reproduction package for our numerical analysis is available here: https://zenodo.org/record/7894030

The high-precision astrometric mission GAIA recently reported the remarkable discovery of a Sun-like star closely orbiting a dark object, with a semi-major axis and period of $1.4\, \rm{AU}$ and $187.8$ days respectively. While the plausible expectation for the central dark object is a black hole, the evolutionary mechanism leading to the formation of such a two-body system is highly challenging. Here, we challenge the scenario of a central black hole and show that the observed orbital dynamics can be explained under fairly general assumptions if the central dark object is a stable clump of bosonic particles of spin-0, or spin-1, known as a boson star. We further explain how future astrometric measurements of similar systems will provide an exciting opportunity to probe the fundamental nature of compact objects and test compact alternatives to black holes., Comment: 11 pages, 4 figures. Comments are very welcome

General extensions of General Relativity (GR) based on bona fide degrees of freedom predict a fifth force which operates within massive objects, opening up an exciting opportunity to perform precision tests of gravity at stellar scales. Here, focusing on general scalar-tensor theories for dark energy, we utilize the Sun as our laboratory and search for imprints of the fifth-force effect on the solar equilibrium structure. With analytic results and numerical simulations, we explain how the different solar regions offer powerful ways to test gravity. Accounting for the delicate interplay between fifth force and solar microphysics such as opacity, diffusion, equation of state and metallicity, we demonstrate that the fifth force still leaves a sharp signature on the solar sound speed, in a region where simple estimates of input physics uncertainties become negligible. For general scalar-field extensions of GR, known as (U-)DHOST, based solely on the observational helioseismic errors, our analysis at the equilibrium level allows to place an approximate constraint on the fifth-force coupling strength of $-10^{-3} \lesssim \mathcal{Y} \lesssim 5\cdot 10^{-4}$ at $2\sigma$. This result improves previous stellar constraints by $\sim 3$ orders of magnitude, and should be confirmed and improved by future helioseismic inversions in modified gravity combined with an elaborate accounting of theoretical uncertainties. Our analysis can be applied to a wide set of theories beyond GR, and also paves the way for helioseismic analyses in this context. In this regard, we discuss how the solar radiative and convective zone can be employed as promising laboratories to test generic theories of gravity., Comment: 13 pages, 10 figures. Comments are welcome

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of GWs can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas., Comment: Accepted in: Living Reviews in Relativity

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe.

The luminosity of the Tip of the Red Giant Branch (TRGB) is instrumental for the construction of the distance ladder, and its accurate modelling is key for determining the local Hubble parameter. In this work, we present an extensive quantitative analysis of the TRGB luminosity, accounting for virtually all input physics that affect it: chemical composition, opacity, diffusion, nuclear reaction rates, electron screening, neutrinos, convection efficiency, boundary conditions and mass loss, amongst others. Our analysis is based on a newly produced grid of $\sim 3\times 10^6$ TRGB models, evolved from pre-main sequence up to the helium ignition at the TRGB, and covering a wide range of metallicity (Z = 0.0001-0.02) and initial mass (M = 0.8-1.4 $M_{\odot}$). Through a Monte-Carlo analysis, we study the systematic variation of the TRGB luminosity due to the combined effect of all above input physics, and show that a maximum theoretical uncertainty of about $1.6 \%$ is still present on the current generation of models, dominated by systematics of radiative opacity. Results are also provided in several photometric bands. As a by-product of our analysis, we demonstrate robust evidence for the linear response of the Tip luminosity to individual changes of input physics, which can significantly simplify future analyses. A comparison of our results with other stellar evolution codes shows excellent agreement, while our grid of models is available upon reasonable requests., Comment: 17 pages, 10 figures. Comments are welcome

The propagation speed of gravitational waves, $c_T$, has been tightly constrained by the binary neutron star merger GW170817 and its electromagnetic counterpart, under the assumption of a frequency-independent $c_T$. Drawing upon arguments from Effective Field Theory and quantum gravity, we discuss the possibility that modifications of General Relativity allow for transient deviations of $c_T$ from the speed of light at frequencies well below the band of current ground-based detectors. We motivate two representative Ans\"atze for $c_T(f)$, and study their impact upon the gravitational waveforms of massive black hole binary mergers detectable by the LISA mission. We forecast the constraints on $c_T(f)$ obtainable from individual systems and a population of sources, from both inspiral and a full inspiral-merger-ringdown waveform. We show that LISA will enable us to place stringent independent bounds on departures from General Relativity in unexplored low-frequency regimes, even in the absence of an electromagnetic counterpart., Comment: 38+20 pages, 22 figures. V2: Analysis improved, to be published in JCAP

We summarize the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with ESA and national space and research funding agencies., Comment: Summary of the Community Workshop on Cold Atoms in Space and corresponding Road-map: https://indico.cern.ch/event/1064855/

We use high-precision combined strong/weak lensing and kinematics measurements of the total mass profiles of the observed galaxy clusters MACS~J1206.2-0847 and Abell~S1063, to constrain the relativistic sector of the general DHOST dark energy theories, which exhibit a partial breaking of the so called Vainsthein screening mechanism, on the linear level of scalar fluctuations around a cosmological background. In particular, by using the \textsc{MG-MAMMPOSSt} framework developed in Pizzuti et al. 2021, for the kinematics analysis of member galaxies in clusters along with lensing mass profile reconstructions, we provide new constraints on the coupling $Y_2$ which governs the theory's relativistic contribution to the lensing potential. The new bound from the combination of kinematics and lensing measurements of MACS 1206, $Y_2=-0.12^{+0.66}_{-0.67}$ at $2\sigma$, provides about a 2-fold improvement on previous constraints. In the case of Abell~S1063 a $>2\sigma$ tension with the GR expectation arises. We discuss this in some detail, and we investigate the possible sources of systematics which can explain the tension. We further discuss why the combination of kinematics of member galaxies with lensing is capable of providing much tighter bounds compared to kinematics or lensing alone, and we explain how the number density profile of tracers, as well as the choice of the velocity anisotropy profile affects the final results., Comment: 11 pages, 11 figures. Submitted to MNRAS

General Relativity and the $\Lambda$CDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. All extended theories and scenarios are first examined under the light of theoretical consistency, and then are applied to various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology are able to offer recently. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature. This work is a Review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. Its realization was performed in the framework of the COST European Action ``Cosmology and Astrophysics Network for Theoretical Advances and Training Actions''., Comment: 543 pages

We present an upgraded version of \textsc{MG-MAMPOSSt}, an extension of the \textsc{MAMPOSSt} algorithm that performs Bayesian fits of models of mass and velocity anisotropy profiles to the distribution of tracers in projected phase space, to handle modified gravity models and constrain their parameters. The new version implements two distinct types of gravity modifications, namely general chameleon and Vainshtein screening, and is further equipped with a Monte-Carlo-Markov-Chain module for an efficient parameter space exploration. The program is complemented by the \textsc{ClusterGEN} code, capable of producing mock galaxy clusters under the assumption of spherical symmetry, dynamical equilibrium, and Gaussian local velocity distribution functions as in \textsc{MAMPOSSt}. We demonstrate the potential of the method by analysing a set of synthetic, isolated spherically-symmetric dark matter haloes, focusing on the statistical degeneracies between model parameters. Assuming the availability of additional lensing-like information, we forecast the constraints on the modified gravity parameters for the two models presented, as expected from joint lensing+internal kinematics analyses, in view of upcoming galaxy cluster surveys. In Vainshtein screening, we forecast the weak lensing effect through the estimation of the full convergence-shear profile. For chameleon screening, we constrain the allowed region in the space of the two free parameters of the model, further focusing on the $f(\mathcal{R})$ subclass to obtain realistic bounds on the background field $|f_{\mathcal{R}0}|$. Our analysis demonstrates the complementarity of internal kinematics and lensing probes for constraining modified gravity theories, and how the bounds on Vainshtein-screened theories improve through the combination of the two probes., Comment: 19 pages, 13 figures, accepted for publication on MNRAS. For v3 : an error in the acknowledgements of v2 has been corrected. A significant extension about lensing in Vainshtein screening has been added compared to v1

We propose helioseismology as a new, precision probe of fifth forces at astrophysical scales, and apply it on the most general scalar-tensor theories for dark energy, known as Degenerate Higher-Order Scalar-Tensor theories (DHOST). We explain how the effect of the fifth force on the solar interior leaves an observable imprint on the acoustic oscillations, and under certain assumptions we numerically compute the non-radial pulsation eigenfrequencies within modified gravity. We illustrate its constraining power by showing that helioseismic observations have the potential to improve constraints on the strength of the fifth force by more than $2$ orders of magnitude, as $-1.8 \cdot 10^{-3} \leq Y \leq 1.2 \cdot 10^{-3}$ (at $2\sigma$). This in turn would suggest constraints of similar order for the theory's free functions around a cosmological background ($\alpha_{\text{H}}, \beta_{1}$)., Comment: 5 pages + references, 4 figures. Version published in Physical Review Letters

Since the very beginning of astronomy the location of objects on the sky has been a fundamental observational quantity that has been taken for granted. While precise two dimensional positional information is easy to obtain for observations in the electromagnetic spectrum, the positional accuracy of current and near future gravitational wave detectors is limited to between tens and hundreds of square degrees, which makes it extremely challenging to identify the host galaxies of gravitational wave events or to confidently detect any electromagnetic counterparts. Gravitational wave observations provide information on source properties and distances that is complementary to the information in any associated electromagnetic emission and that is very hard to obtain in any other way. Observing systems with multiple messengers thus has scientific potential much greater than the sum of its parts. A gravitational wave detector with higher angular resolution would significantly increase the prospects for finding the hosts of gravitational wave sources and triggering a multi-messenger follow-up campaign. An observatory with arcminute precision or better could be realised within the Voyage 2050 programme by creating a large baseline interferometer array in space and would have transformative scientific potential. Precise positional information of standard sirens would enable precision measurements of cosmological parameters and offer new insights on structure formation; a high angular resolution gravitational wave observatory would allow the detection of a stochastic background and resolution of the anisotropies within it; it would also allow the study of accretion processes around black holes; and it would have tremendous potential for tests of modified gravity and the discovery of physics beyond the Standard Model., Comment: 26 pages, 2 figures. White paper submitted to ESA's Voyage 2050 call on behalf of the LISA Consortium 2050 Task Force

The gravitational slip parameter is an important discriminator between large classes of gravity theories at cosmological and astrophysical scales. In this work we use a combination of simulated information of galaxy cluster mass profiles, inferred by Strong+Weak lensing analyses and by the study of the dynamics of the cluster member galaxies, to reconstruct the gravitational slip parameter $\eta$ and predict the accuracy with which it can be constrained with current and future galaxy cluster surveys. Performing a full-likelihood statistical analysis, we show that galaxy cluster observations can constrain $\eta$ down to the percent level already with a few tens of clusters. We discuss the significance of possible systematics, and show that the cluster masses and numbers of galaxy members used to reconstruct the dynamics mass profile have a mild effect on the predicted constraints., Comment: 18 pages plus references, 8 Figures

The goal of this short report is to summarise some key results based on our previous works on model independent tests of gravity at large scales in the Universe, their connection with the properties of gravitational waves, and the implications of the recent measurement of the speed of tensors for the phenomenology of general families of gravity models for dark energy., Comment: 11 pages plus references. Based on a talk given at the 15th Marcel Grossmann meeting

We use the most recent, complete and independent measurements of masses and radii of white dwarfs in binaries to bound the class of non-trivial modified gravity theories, viable after GW170817/GRB170817, using its effect on the mass-radius relation of the stars. We show that the uncertainty in the latest data is sufficiently small that residual evolutionary effects, most notably the effect of core composition, finite temperature and envelope structure, must now accounted for if correct conclusions about the nature of gravity are to be made. We model corrections resulting from finite temperature and envelopes to a base Hamada-Salpeter cold equation of state and derive consistent bounds on the possible modifications of gravity in the stars' interiors, finding that $Y< 0.14$ at 95\% confidence, an improvement of a factor of three with respect to previous bounds. Finally, our analysis reveals some fundamental degeneracies between the theory of gravity and the precise chemical makeup of white dwarfs., Comment: 10 pages plus references, 5 figures

The recent discovery of a $\gamma$-ray counterpart to a gravitational wave event has put extremely stringent constraints on the speed of gravitational waves at the present epoch. In turn, these constraints place strong theoretical pressure on potential modifications of gravity, essentially allowing only a conformally-coupled scalar to be active in the present Universe. In this paper, we show that direct detection of gravitational waves from optically identified sources can also measure or constrain the strength of the conformal coupling in scalar--tensor models through the time variation of the Planck mass. As a first rough estimate, we find that the LISA satellite can measure the dimensionless time variation of the Planck mass (the so-called parameter $\alpha_M$) at redshift around 1.5 with an error of about 0.03 to 0.13, depending on the assumptions concerning future observations. Stronger constraints can be achieved once reliable distance indicators at $z>2$ are developed, or with GW detectors that extend the capabilities of LISA, like the proposed Big Bang Observer. We emphasize that, just like the constraints on the gravitational speed, the bound on $\alpha_M$ is independent of the cosmological model., Comment: 4 pages, 1 figure. v2: Minor clarifications in the text, new references added. Version published in JCAP

In the first part of this paper we critically examine the ultra-violet implications of theories that exhibit Vainshtein screening, taking into account both the standard Wilsonian perspective as well as more exotic possibilities. Aspects of this discussion draw on results from the second part of the paper in which we perform a general study of derivatively coupled scalar theories using non-perturbative exact renormalisation group techniques, which are of interest independently of their application to modified gravity. In this context, we demonstrate the suppression of quantum corrections within the Vainshtein radius and discuss the potential relation with the classicalisation conjecture. We question whether the latter can be considered a realistic candidate for UV completion of large-scale modifications of gravity on account of a dangerously low classicalisation/strong coupling scale., Comment: 10 pages, 6 figures. v2: Minor clarifying comments added in the text, version to appear in JCAP

The coincident detection of gravitational waves (GW) and a gamma-ray burst from a merger of neutron stars has placed an extremely stringent bound on the speed of GW. We showed previously that the presence of gravitational slip ($\eta$) in cosmology is intimately tied to modifications of GW propagation. This new constraint implies that the only remaining viable source of gravitational slip is a conformal coupling to gravity in scalar-tensor theories, while viable vector-tensor theories cannot now generate gravitational slip at all. We discuss structure formation in the remaining viable models, demonstrating that (i) the dark-matter growth rate must now be at least as fast as in GR, with the possible exception of the beyond Horndeski model. (ii) If there is any scale-dependence at all in the slip parameter, it is such that it takes the GR value at large scales. We show a consistency relation which must be violated if gravity is modified., Comment: 4 pages

We present for the first time an explicit exposition of quantum corrections within the cubic Galileon theory including the effect of quantum gravity, in a background- and gauge-invariant manner, employing the field-reparametrisation approach of the covariant effective action at 1-loop. We show that the consideration of gravitational effects in combination with the non-linear derivative structure of the theory reveals new interactions at the perturbative level, which manifest themselves as higher-operators in the associated effective action, which' relevance is controlled by appropriate ratios of the cosmological vacuum and the Galileon mass scale. The significance and concept of the covariant approach in this context is discussed, while all calculations are explicitly presented., Comment: 18 pages plus references, 1 figure

In many generalized models of gravity, perfect fluids in cosmology give rise to gravitational slip. Simultaneously, in very broad classes of such models, the propagation of gravitational waves is altered. We investigate the extent to which there is a one-to-one relationship between these two properties in three classes of models with one extra degree of freedom: scalar (Horndeski and beyond), vector (Einstein-Aether) and tensor (bimetric). We prove that in bimetric gravity and Einstein-Aether, it is impossible to dynamically hide the gravitational slip on all scales whenever the propagation of gravitational waves is modified. Horndeski models are much more flexible, but it is nonetheless only possible to hide gravitational slip dynamically when the action for perturbations is tuned to evolve in time toward a divergent kinetic term. These results provide an explicit, theoretical argument for the interpretation of future observations if they disfavoured the presence of gravitational slip., Comment: 14 pages; v2 reflects that accepted for publication in PRD. Discussion of proof for Horndeski significantly improved

We derive the 1-loop effective action of the cubic Galileon coupled to quantum-gravitational fluctuations in a background and gauge-independent manner, employing the covariant framework of DeWitt and Vilkovisky. Although the bare action respects shift symmetry, the coupling to gravity induces an effective mass to the scalar, of the order of the cosmological constant, as a direct result of the non-flat field-space metric, the latter ensuring the field-reparametrization invariance of the formalism. Within a gauge-invariant regularization scheme, we discover novel, gravitationally induced non-Galileon higher-derivative interactions in the effective action. These terms, previously unnoticed within standard, non-covariant frameworks, are not Planck suppressed. Unless tuned to be sub-dominant, their presence could have important implications for the classical and quantum phenomenology of the theory., Comment: 5 pages plus references

We use the Wilsonian functional Renormalisation Group (RG) to study quantum corrections for the Higgs inflationary action including the effect of gravitons, and analyse the leading-order quantum gravitational corrections to the Higgs' quartic coupling, as well as its non-minimal coupling to gravity and Newton's constant, at the inflationary regime and beyond. We explain how within this framework the effect of Higgs and graviton loops can be sufficiently suppressed during inflation, and we also place a bound on the corresponding value of the infrared RG cut-off scale during inflation. Finally, we briefly discuss the potential embedding of the model within the scenario of Asymptotic Safety, while all main equations are explicitly presented., Comment: 17 pages + Appendices, 1 figure. v2: Some typos corrected and references added, accepted for publication in JCAP

Despite its continued observational successes, there is a persistent (and growing) interest in extending cosmology beyond the standard model, $\Lambda$CDM. This is motivated by a range of apparently serious theoretical issues, involving such questions as the cosmological constant problem, the particle nature of dark matter, the validity of general relativity on large scales, the existence of anomalies in the CMB and on small scales, and the predictivity and testability of the inflationary paradigm. In this paper, we summarize the current status of $\Lambda$CDM as a physical theory, and review investigations into possible alternatives along a number of different lines, with a particular focus on highlighting the most promising directions. While the fundamental problems are proving reluctant to yield, the study of alternative cosmologies has led to considerable progress, with much more to come if hopes about forthcoming high-precision observations and new theoretical ideas are fulfilled., Comment: 99 pages, 8 figures. Version published in Physics of the Dark Universe

It is a well known result that any formulation of unimodular gravity is classically equivalent to General Relativity (GR), however a debate exists in the literature about this equivalence at the quantum level. In this work, we investigate the UV quantum structure of a diffeomorphism invariant formulation of unimodular gravity using functional renormalisation group methods in a Wilsonian context. We show that the effective action of the unimodular theory acquires essentially the same form with that of GR in the UV, as well as that both theories share similar UV completions within the framework of the asymptotic safety scenario for quantum gravity. Furthermore, we find that in this context the unimodular theory can appear to be non--predictive due to an increasing number of relevant couplings at high energies, and explain how this unwanted feature is in the end avoided., Comment: 11 pages plus Appendix; Some clarifying comments added, results unchanged; Version to appear in Physical Review D

We discuss unimodular gravity at a classical level, and in terms of its extension into the UV through an appropriate path integral representation. Classically, unimodular gravity is simply a gauge fixed version of General Relativity (GR), and as such it yields identical dynamics and physical predictions. We clarify this and explain why there is no sense in which it can "bring a new perspective" to the cosmological constant problem. The quantum equivalence between unimodular gravity and GR is more of a subtle question, but we present an argument that suggests one can always maintain the equivalence up to arbitrarily high momenta. As a corollary to this, we argue that whenever inequivalence is seen at the quantum level, that just means we have defined two different quantum theories that happen to share a classical limit., Comment: 5 pages; v2: Some clarifying comments added. Version to appear in European Physical Journal C

We make precise the heretofore ambiguous statement that anisotropic stress is a sign of a modification of gravity. We show that in cosmological solutions of very general classes of models extending gravity --- all scalar-tensor theories (Horndeski), Einstein-Aether models and bimetric massive gravity --- a direct correspondence exists between perfect fluids apparently carrying anisotropic stress and a modification in the propagation of gravitational waves. Since the anisotropic stress can be measured in a model-independent manner, a comparison of the behavior of gravitational waves from cosmological sources with large-scale-structure formation could in principle lead to new constraints on the theory of gravity., Comment: 4 pages plus references. Version to appear in Physical Review Letters

We revisit Starobinsky inflation in a quantum gravitational context, by means of the exact Renormalisation Group (RG). We calculate the non-perturbative beta functions for Newton's `constant' G and the dimensionless R^2 coupling, and show that there exists an attractive UV fixed point where the latter one vanishes but not the former one, and we provide the corresponding beta functions. The smallness of the R^2 coupling, required for agreement with inflationary observables, is naturally ensured by its vanishing at the UV fixed point, ensuring the smallness of the primordial fluctuations, as well as providing a theoretical motivation for the initial conditions needed for successful inflation in this context. We discuss the corresponding RG dynamics, showing both how inflationary and classical observations define the renormalisation conditions for the couplings, and also how the UV regime is connected with lower energies along the RG flow. Finally, we discuss the consistency of our results when higher order curvature corrections are included, and show that they are robust to the inclusion of R^3 corrections., Comment: 14 pages, 4 figures. v.3: This version matches the one published in PRD. The results and conclusions remain the same. Some clarifying comments, new references, and three new figures have been added. A new section investigating the significance of higher-order operators has been introduced

We consider the consequences of having no prior knowledge of the true dark energy model for the interpretation of cosmological observations. The magnitude of redshift-space distortions and weak-lensing shear is determined by the metric on the geodesics of which galaxies and light propagate. We show that, given precise enough observations, we can use these data to completely reconstruct the metric on our past lightcone and therefore to measure the scale- and time-dependence of the anisotropic stress and the evolution of the gravitational potentials in a model-independent manner. Since both dark matter and dark energy affect the visible sector only through the gravitational field they produce, they are inseparable without a model for dark energy: galaxy bias cannot be measured and therefore the distribution of dark matter determined; the peculiar velocity of dark matter can be identified with that of the galaxies only when the equivalence principle holds. Given these limitations, we show how one can nonetheless build tests for classes of dark energy models which depend on making measurements at multiple scales at a particular redshift. They are null tests on the model-independent observables, do not require modeling evolution in time and do not require any parametrization of the free functions of these models, such as the sound speed. We show how one can rule out or constrain the whole class of the most-general scalar-tensor theories even without assuming the quasi-static limit., Comment: 11 pages; v2 reflect version accepted for publication in PRD. Minor additions discussing the feasibility of proposed tests and describing effect of more than one degree of freedom for dark energy

The aim of this paper is to answer the following two questions: (1) Given cosmological observations of the expansion history and linear perturbations in a range of redshifts and scales as precise as is required, which of the properties of dark energy could actually be reconstructed without imposing any parameterization? (2) Are these observables sufficient to rule out not just a particular dark energy model, but the entire general class of viable models comprising a single scalar field? This paper bears both good and bad news. On one hand, we find that the goal of reconstructing dark energy models is fundamentally limited by the unobservability of the present values of the matter density Omega_m0, the perturbation normalization sigma_8 as well as the present matter power spectrum. On the other, we find that, under certain conditions, cosmological observations can nonetheless rule out the entire class of the most general single scalar-field models, i.e. those based on the Horndeski Lagrangian., Comment: 9 pages. v2 reflects version accepted for publication in PRD (includes additional discussion of geometrical distance measures, new appendix on general scalar-tensor theories and new references)

We present a new prescription for analysing cosmological perturbations in a more-general class of scalar-field dark-energy models where the energy-momentum tensor has an imperfect-fluid form. This class includes Brans-Dicke models, f(R) gravity, theories with kinetic gravity braiding and generalised galileons. We employ the intuitive language of fluids, allowing us to explicitly maintain a dependence on physical and potentially measurable properties. We demonstrate that hydrodynamics is not always a valid description for describing cosmological perturbations in general scalar-field theories and present a consistent alternative that nonetheless utilises the fluid language. We apply this approach explicitly to a worked example: k-essence non-minimally coupled to gravity. This is the simplest case which captures the essential new features of these imperfect-fluid models. We demonstrate the generic existence of a new scale separating regimes where the fluid is perfect and imperfect. We obtain the equations for the evolution of dark-energy density perturbations in both these regimes. The model also features two other known scales: the Compton scale related to the breaking of shift symmetry and the Jeans scale which we show is determined by the speed of propagation of small scalar-field perturbations, i.e. causality, as opposed to the frequently used definition of the ratio of the pressure and energy-density perturbations., Comment: 40 pages plus appendices. v2 reflects version accepted for publication in JCAP (new summary of notation, extra commentary on choice of gauge and frame, extra references to literature)

We explore the cosmological dynamics of an effective f(R) model constructed from a renormalisation group (RG) improvement of the Einstein--Hilbert action, using the non-perturbative beta functions of the exact renormalisation group equation. The resulting f(R) model has some remarkable properties. It naturally exhibits an unstable de Sitter era in the ultraviolet (UV), dynamically connected to a stable de Sitter era in the IR, via a period of radiation and matter domination, thereby describing a non-singular universe. We find that the UV de Sitter point is one of an infinite set, which make the UV RG fixed point inaccessible to classical cosmological evolution. In the vicinity of the fixed point, the model behaves as R^2 gravity, while it correctly recovers General Relativity at solar system scales. In this simplified model, the fluctuations are too large to be the observed ones, and more ingredients in the action are needed., Comment: 15 pages, 8 figures

The existence of anisotropic stress of a purely geometrical origin seems to be a characteristic of higher order gravity models, and has been suggested as a probe to test these models observationally, for example in weak lensing experiments. In this paper, we seek to find a class of higher order gravity models of f(R,G) type that would give us a zero anisotropic stress and study the consequences for the viability of the actual model. For the special case of a de Sitter background, we identify a subclass of models with the desired property. We also find a direct link between anisotropic stress and the stability of the model as well as the presence of extra degrees of freedom, which seems to be a general feature of higher order gravity models. Particularly, setting the anisotropic stress equal to zero for a de Sitter background leads to a singularity that makes it impossible to reach the de Sitter evolution., Comment: 15 pages, v2: Minor changes in the text, typos corrected

We revisit the dynamical equivalence between different representations of vacuum modified gravity models in view of Legendre transformations. The equivalence is discussed for both bulk and boundary space, by including in our analysis the relevant Gibbons-Hawking terms. In the f(R) case, the Legendre transformed action coincides with the usual Einstein frame one. We then re-express the R+f(G) action, where G is the Gauss-Bonnet term, as a second order theory with a new set of field variables, four tensor fields and one scalar and study its dynamics. For completeness, we also calculate the conformal transformation of the full Jordan frame R+f(G) action. All the appropriate Gibbons-Hawking terms are calculated explicitly., Comment: 17 pages; v3: Revised version. New comments added in Sections 3 & 5. New results added in Section 6. Version to appear in Class. Quantum Gravity