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In the context of Chameleon gravity, we present a semi-analytical solution of the chameleon field profile in accurately modelled galaxy cluster's mass components, namely: the stellar mass of the Brightest Cluster Galaxy (BCG), the baryonic mass in galaxies (other than the BCG), the mass of the Intra-Cluster Medium (ICM) and the diffuse cold dark matter (CDM). The obtained semi-analytic profile is validated against the numerical solution of the chameleon field equation and implemented in the \textsc{MG-MAMPOSSt} code for kinematic analyses of galaxy clusters in modified gravity scenarios. By means of mock halos, simulated both in GR and in modified gravity, we show that the combination of velocities and positions of cluster member galaxies, along with data of the stellar velocity dispersion profile of the BCG, can impose constraints on the parameter space of the Chameleon model; for a cluster generated in GR, these constraints are at the same level as a joint lensing+kinematics analysis of a cluster modelled with a single mass profile, without the BCG data., Comment: 22 pages, 10 figures

Refracted Gravity (RG) is a a classical theory of gravity where a gravitational permittivity $ a monotonically-increasing function of the local density rho , is introduced in the Poisson equation to mimic the effect of dark matter at astrophysical scales. We use high precision spectroscopic data of two massive galaxy clusters, MACS J1206.2-0847 at redshift z=0.44, and Abell S1063 (RXC J2248.7-4431) at z=0.35, to determine the total gravitational potential in the context of RG and to constrain the three, supposedly universal, free parameters of this model. Using an upgraded version of the MG-MAMPOSSt algorithm, we perform a kinematic analysis which combines the velocity distribution of the cluster galaxies and the velocity dispersion profile of the stars within the Brightest Cluster Galaxy (BCG). The unprecedented dataset used has been obtained by an extensive spectroscopic campaign carried out with the VIMOS and MUSE spectrographs at the ESO VLT. We found that RG describes the kinematics of these two clusters as well as Newtonian gravity, although the latter is slightly preferred. However, (i) each cluster requires a different set of the three free RG parameters, and (ii) the two sets are inconsistent with other results in the literature at different scales. We discuss the limitation of the method used to constrain the RG parameters as well as possible systematic effects which can give rise to the observed tension, notably deviations from the spherical symmetry and from the dynamical equilibrium of the clusters., Comment: 10 pages, 6 figures. Submitted to A&A

The Cluster HEritage project with XMM-Newton - Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE) is a programme to study a minimally biased sample of 118 galaxy clusters detected by Planck through the Sunyaev-Zeldovich effect. Accurate and precise mass measurements are required to exploit CHEX-MATE as an astrophysical laboratory and a calibration sample for cosmological probes in the era of large surveys. We measured masses based on the galaxy dynamics, which are highly complementary to weak-lensing or X-ray estimates. We analysed the sample with a uniform pipeline that is stable both for poorly sampled or rich clusters - using spectroscopic redshifts from public (NED, SDSS, and DESI) or private archives - and dedicated observational programmes. We modelled the halo mass density and the anisotropy profile. Membership is confirmed with a cleaning procedure in phase space. We derived masses from measured velocity dispersions under the assumed model. We measured dynamical masses for 101 CHEX-MATE clusters with at least ten confirmed members within the virial radius r_200c. Estimated redshifts and velocity dispersions agree with literature values when available. Validation with weak-lensing masses shows agreement within 8+-16(stat.)+-5(sys.)%, and confirms dynamical masses as an unbiased proxy. Comparison with {\it Planck} masses shows them to be biased low by 34+-3(stat.)+-5(sys.)%. A follow-up spectroscopic campaign is underway to cover the full CHEX-MATE sample., Comment: 18 pages, 12 figures. In press on A&A

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

The chameleon screening mechanism has been constrained many a time using dynamic and kinematic galaxy cluster observables. Current constraints are, however, insensitive to different mass components within galaxy clusters and have been mainly focused on a single mass density profile, the Navarro-Frenk-While mass density model. In this work, we extend the study of the Chameleon screening mechanism in galaxy clusters by considering a series of mass density models, namely: generalized-Navarro-Frenk-While, b-Navarro-Frenk-While, Burket, Isothermal and Einasto. The coupling strength ($\beta$) and asymptotic value of the chameleon field ($\phi_\infty$) are constrained by using kinematics analyses of simulated galaxy clusters, generated both assuming General Relativity and a strong chameleon scenario. By implementing a Bayesian analysis we comprehensively show that the biases introduced due to an incorrect assumption of the mass model are minimal. Similarly, we also demonstrate that a spurious detection of evidence for modifications to gravity is highly unlikely when utilizing the kinematics of galaxy clusters., Comment: 25 pages, 7 Figures, to be submitted to JCAP

Virial-like identities obtained through Derrick's scaling argument are powerful, multi-purpose tools to study general relativistic models. Applications comprise establishing no-go/hair theorems and numerical accuracy tests. In the presence of a horizon (\textit{aka} boundary), the spacetime can be divided into regions, each with its own identity. So far, such identities have only been computed in the region outside the event horizon; however, adding a positive cosmological constant endows an additional boundary (the cosmological horizon), with the region between the latter and the former of particular interest. In this letter, by performing a radial coordinate transformation, we generalise Derrick's scaling argument to compute virial identities \textit{across the whole} non-asymptotically flat spacetimes. The developed method is applied to the entire Reissner-Nordstrom-de Sitter spacetime. A convenient gauge that trivialises the gravitational contribution to the identity between horizons is also found., Comment: 9 pages, 1 Figure

We propose and perform a joint analysis of the two different mass estimates of galaxy clusters, namely the hydrostatic and caustic techniques. Firstly, we show comprehensively that the mass bias between these two techniques can be possibly alleviated when cluster-specific assumptions constrained using the hydrostatic technique are utilized within the caustic technique. While at face value this demotes the caustic technique from a completely independent method, this allows one to further tighten the constraints on the cluster mass and subsequently, allow us to test modifications to gravity. Implementing the aforementioned formalism for two well-observed massive galaxy clusters, A2029 and A2142, we highlight the proof of concept. In the current implementation, we use this method to constrain the Chameleon screening and Vainshtein screening. As anticipated, we show that the joint analysis can help improve the constraints on these modified gravity scenarios., Comment: 17 pages, 9 figures. Agrees with the accepted version, references added

An interesting mechanism for the formation of hairy black holes occurs when a vector field, non-minimally coupled to a source term, grows from a perturbation of the vacuum black hole, \textit{aka} vectorization. Its study has, however, been lacking, in part due to the constant threat of ghost instabilities that have plagued vector fields. In this work, we show evidence that, in a generic family of extended-vector-tensor theories where the vector field is non-minimally coupled to the model's invariant (source term), a spherically symmetric, vectorized black hole always suffers from ghost instabilities. These ultimately turn the process of vectorization astrophysically unviable., Comment: 12 pages

We constrain the Chameleon \textit{screening} mechanism in galaxy clusters, essentially obtaining limits on the coupling strength $\beta$ and the asymptotic value of the field $\phi_{\infty}$. For this purpose, we utilized a collection of the 9 relaxed galaxy clusters within the X-COP compilation in the redshift range of $z \le 0.1$. We implement the formalism assuming an NFW mass profile for the dark matter density and study the degeneracy present between the mass $\M$ and the chameleon coupling with a high degree of improvement in the constraints for excluded parameter space. We recast our constrain to an upper limit on the scalaron field in \fofr sub-class of models of $|f_{R0}|\le 9.2\times 10^{-6}$, using all the nine clusters and $|f_{R0}|\le 1.2\times 10^{-5}$ using only 5 clusters with WL priors taken into account, at a $95\%$ confidence level. These bounds are consistent with existing limits in the literature and tighter than the constraints obtained with the same method by previous studies., Comment: Comments are welcome

This work presents a set of coupled Boltzmann equations describing the intensity and polarisation Stokes parameters of the SGWB. Collision terms, which account for gravitational Compton scattering off of massive objects, are also included. This set resembles that for the CMB Stokes parameters, but the different spin nature of the gravitational radiation and the physics involved in the scattering process determine crucial differences. In this case, due to the Rutherford angular dependence of the cross section, all the SGWB intensity multipoles of order $\ell$ are scattered out, producing outgoing intensity anisotropies of any order $\ell$ if they are present in the incoming radiation. On the other hand, SGWB linear polarisation modes can be expanded in a basis of spherical harmonics with $m=\pm 4$ and $\ell\ge 4$. This means that SGWB polarisation modes can be generated from unpolarised anisotropic radiation only with $m=\pm 4$, therefore requiring at least a hexadecapole anisotropy ($\ell\ge 4$) in the incoming intensity. Assuming a simplified toy model, we solve analytically the set of coupled Boltzmann equations to get explicit expressions for the intensity and polarisation angular power spectra. We confirm the contribution of the gravitational Compton scattering to the SGWB anisoptropies is extremely small for collisions with compact objects in the frequency range of current and upcoming surveys. The system of coupled Boltzmann equations presented here provides a way to an accurate estimate of the total amount of anisotropies generated by multiple SGWB scattering processes off of massive objects, as well as the interplay between polarisation and intensity, during the GW propagation across the LSS of the universe. These results will be useful for the full treatment of the astrophysical SWGB anisotropies in view of upcoming gravitational waves observatories., Comment: 28 pages, 2 tables, 2 figures. Matches the accepted version in JCAP

We present \textsc{MG-MAMPOSSt}, a license-free code to constrain modified gravity models by reconstructing the mass profile of galaxy clusters with the kinematics of the cluster's member galaxies. We describe the main features of the code and we show the capability of the method when the kinematic information is combined with lensing data. We discuss recent results and forecasts on two classes of models currently implemented in the code, characterized by different screening mechanisms, namely, chameleon and Vainshtein screening. We further explore the impact of possible systematics in view of application to the data from upcoming surveys. This proceedings summarizes the results presented at the ALTECOSMOFUN workshop in September 2021., Comment: Proceedings of the ALTECOSMOFUN'21 conference published in Universe, Issue "Alternative Gravities and Fundamental Cosmology"

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

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