General Relativity and the ΛCDM 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.We list 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.
We perform a maximum likelihood kinematic analysis of the two dynamically relaxed galaxy clusters MACS J1206.2-0847 at z = 0.44 and RXC J2248.7-4431 at z = 0.35 to determine the total mass profile in modified gravity models, using a modified version of the MAMPOSSt code of Mamon, Biviano and Boué. Our work is based on the kinematic and lensing mass profiles derived using the data from the Cluster Lensing And Supernova survey with Hubble (hereafter CLASH) and the spectroscopic follow-up with the Very Large Telescope (hereafter CLASH-VLT). We assume a spherical Navarro-Frenk-White (NFW hereafter) profile in order to obtain a constraint on the fifth force interaction range λ for models in which the dependence of this parameter on the environment is negligible at the scale considered (i.e. λ = const) and fixing the fifth force strength to the value predicted in f (R) gravity. We then use information from lensing analysis to put a prior on the other NFW free parameters. In the case of MACSJ 1206 the joint kinematic+lensing analysis leads to an upper limit on the effective interaction range λ ≤ 1.61 Mpc at ∆χ 2 = 2.71 on the marginalized distribution. For RXJ 2248 instead a possible tension with the ΛCDM model appears when adding lensing information, with a lower limit λ ≥ 0.14 Mpc at ∆χ 2 = 2.71. This is consequence of the slight difference between the lensing and kinematic data, appearing in GR for this cluster, that could in principle be explained in terms of modifications of gravity. We discuss the impact of systematics and the limits of our analysis as well as future improvements of the results obtained. This work has interesting implications in view of upcoming and future large imaging and spectroscopic surveys, that will deliver lensing and kinematic mass reconstruction for a large number of galaxy clusters.
We use high-precision kinematic and lensing measurements of the total mass profile of the dynamically relaxed galaxy cluster MACS J1206.2-0847 at z = 0.44 to estimate the value of the ratio η = Ψ/Φ between the two scalar potentials in the linear perturbed Friedmann-Lemaitre-Robertson-Walker metric. An accurate measurement of this ratio, called anisotropic stress, could show possible, interesting deviations from the predictions of the theory of General Relativity, according to which Ψ should be equal to Φ. Complementary kinematic and lensing mass profiles were derived from exhaustive analyses using the data from the Cluster Lensing And Supernova survey with Hubble (CLASH) and the spectroscopic follow-up with the Very Large Telescope (CLASH-VLT). Whereas the kinematic mass profile tracks only the time-time part of the perturbed metric (i.e. only Φ), the lensing mass profile reflects the contribution of both time-time and space-space components (i.e. the sum Φ + Ψ). We thus express η as a function of the mass profiles and perform our analysis over the radial range 0.5 Mpc ≤ r ≤ r 200 = 1.96 Mpc. Using a spherical Navarro-Frenk-White mass profile, which well fits the data, we obtain η(r 200 ) = 1.01 +0.31 −0.28 at the 68% C.L. We discuss the effect of assuming different functional forms for mass profiles and of the orbit anisotropy in the kinematic reconstruction. Interpreting this result within the well-studied f (R) modified gravity model, the constraint on η translates into an upper bound to the interaction length (inverse of the scalaron mass) smaller than 2 Mpc. This tight constraint on the f (R) interaction range is however substantially relaxed when systematic uncertainties in the analysis are considered. Our analysis highlights the potential of this method to detect deviations from general relativity, while calling for the need of further high-quality data on the total mass distribution of clusters and improved control on systematic effects.
We present an upgraded version of MG-MAMPOSSt, an extension of the 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 ClusterGEN code, capable of producing mock galaxy clusters under the assumption of spherical symmetry, dynamical equilibrium, and Gaussian local velocity distribution functions as in 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.
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