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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

We analyse the dynamical state of the galaxy clusters Abell 76 and Abell 1307 from the optical point of view, presenting a coherent scenario that responds to the X-ray emissions observed in these structures. Our study is based on 231 and 164 spectroscopic redshifts, for the clusters A76 and A1307, respectively. We find that A76 and A1307 are two galaxy clusters at $z=0.0390$ and 0.0815, respectively, with velocity dispersions of $650 \pm 56$ km s$^{-1}$ and $863 \pm 85$ km s$^{-1}$, and showing velocity distributions following, in practice, Gaussian profiles. From our dynamical analysis, X-ray studies and SZ-Planck emission, we obtain a mean total mass M$_{500} = 1.7 \pm 0.6 \cdot 10^{14}$ M$_{\odot}$ and $3.5 \pm 1.3 \cdot 10^{14}$ M$_{\odot}$ for A76 and A1307, respectively. We find that the spatial distribution of likely cluster members in the case of A76 is very anisotropic, while A1307 shows a compact distribution of galaxies, but double peaked and elongated in the south-north direction. we compare the XMM-Newton surface brightness maps with galaxy distributions and see that both distributions are correlated. We reconstruct the total mass profile and velocity anisotropy of both clusters by analysing the full projected phase space, through the MG-MAMPOSSt code. Our study reveals a slight indication of radial orbits for A76, while A1307 seems to prefer more isotropic orbits in the whole cluster range. Summarizing, A76 represent a typical young cluster, in an early stage of formation, with a very low X-ray surface brightness but high temperature showing a very anisotropic galaxy distribution. A1307 is however more consolidated and massive showing in-homogeneous galaxy distribution and an asymmetric X-ray emission, which suggest a scenario characterised by recent minor mergers., Comment: 14 pages and 12 figures. Tables 1 and 2 are included as electronic form at the CDS

The Euclid mission will measure cosmological parameters with unprecedented precision. To distinguish between cosmological models, it is essential to generate realistic mock observables from cosmological simulations that were run in both the standard $\Lambda$-cold-dark-matter ($\Lambda$CDM) paradigm and in many non-standard models beyond $\Lambda$CDM. We present the scientific results from a suite of cosmological N-body simulations using non-standard models including dynamical dark energy, k-essence, interacting dark energy, modified gravity, massive neutrinos, and primordial non-Gaussianities. We investigate how these models affect the large-scale-structure formation and evolution in addition to providing synthetic observables that can be used to test and constrain these models with Euclid data. We developed a custom pipeline based on the Rockstar halo finder and the nbodykit large-scale structure toolkit to analyse the particle output of non-standard simulations and generate mock observables such as halo and void catalogues, mass density fields, and power spectra in a consistent way. We compare these observables with those from the standard $\Lambda$CDM model and quantify the deviations. We find that non-standard cosmological models can leave significant imprints on the synthetic observables that we have generated. Our results demonstrate that non-standard cosmological N-body simulations provide valuable insights into the physics of dark energy and dark matter, which is essential to maximising the scientific return of Euclid., Comment: 22 pages, 7 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, 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

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

We analyse a sample of 244 ram-pressure-stripped candidate galaxy members within the virial radius of 62 nearby clusters, to determine their velocity anisotropy profile $\beta(r)$. We use previously determined mass profiles for the 62 clusters to build an ensemble cluster by stacking the 62 cluster samples in projected phase-space. We solve the Jeans equation for dynamical equilibrium by two methods, MAMPOSSt and the Jeans inversion technique, and determine $\beta(r)$ both in parametric form and non-parametrically. The two methods consistently indicate that the orbits of the ram-pressure-stripped candidates are increasingly radial with distance from the cluster center, from almost isotropic ($\beta \simeq 0$) at the center, to very radial at the virial radius ($\beta \simeq 0.7$). The orbits of cluster galaxies undergoing ram-pressure stripping are similar to those of spiral cluster galaxies, but more radially elongated at large radii., Comment: The Astrophysical Journal, in press

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

The inner slope (gammadm) of the dark matter (DM) density profile of cosmological halos carries information about the properties of DM and/or baryonic processes affecting the halo gravitational potential. Cold DM cosmological simulations predict steep inner slopes, gammadm~1. We test this prediction on the MACS J1206.2-0847 cluster at redshift z=0.44, whose DM density profile was claimed to be cored at the center. We determine the cluster DM density profile from 2 kpc from the cluster center to the virial radius (~2 Mpc), using the velocity distribution of ~500 cluster galaxies and the internal velocity dispersion profile of the Brightest Cluster Galaxy (BCG), obtained from VIMOS@VLT and MUSE@VLT data. We solve the Jeans equation of dynamical equilibrium using an upgraded version of the MAMPOSSt method. The total mass profile is modeled as a sum of a generalized-NFW profile that describes the DM component, allowing for a free inner slope of the density profile, a Jaffe profile that describes the BCG stellar mass component, and a non-parametric baryonic profile that describes the sum of the remaining galaxy stellar mass and of the hot intra-cluster gas mass. Our total mass profile is in remarkable agreement with independent determinations based on X-ray observations and strong lensing. We find gammadm=0.7 (-0.1 +0.2) (68\% confidence levels), consistent with predictions from recent LambdaCDM cosmological numerical simulations., Comment: ApJ, 958, 148. Minor modifications to the text, two figures and the table, with respect to the previous version

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"

The \textsc{MG-MAMPOSSt} code is a license-free \textsc{Fortran95} code to perform tests of General Relativity (GR) through the analyses of kinematical data of galaxy clusters based on the Jeans' equation. The code is based on the \textsc{MAMPOSSt} method, and extends the original code through new parametrisations of the gravitational potential for general families of gravity theories beyond GR aimed to explain dark energy. \textsc{MG-MAMPOSSt} is further supplemented with a new capability to produce weak lensing forecasts for joint kinematic+lensing analysis. This document provides a technical description of the code's new features, functionality with respect to the original version, and instructions on its installation and use. Finally, we explain how the code could be further modified to include a wider family of gravity models and/or density profiles, that could allow its application in broader theoretical frameworks as well as other physical systems such as stellar clusters. A detailed forecast analysis for the modified gravity models currently implemented in the code can be found in the paper of Pizzuti et al., 2021., Comment: 23 pages, two figures. Techinical manual to be submitted to JOSS

The trend towards specialization of software and hardware - fuelled by the end of Moore's law and the still accelerating interest in domain-specific computing, such as machine learning - forces us to radically rethink our compiler designs. The era of a universal compiler framework built around a single one-size-fits-all intermediate representation (IR) is over. This realization has sparked the creation of the MLIR compiler framework that empowers compiler engineers to design and integrate IRs capturing specific abstractions. MLIR provides a generic framework for SSA-based IRs, but it doesn't help us to decide how we should design IRs that are easy to develop, to work with and to combine into working compilers. To address the challenge of IR design, we advocate for a language-oriented compiler design that understands IRs as formal programming languages and enforces their correct use via an accompanying type system. We argue that programming language techniques directly guide extensible IR designs and provide a formal framework to reason about transforming between multiple IRs. In this paper, we discuss the design of the Shine compiler that compiles the high-level functional pattern-based data-parallel language RISE via a hybrid functional-imperative intermediate language to C, OpenCL, and OpenMP. We compare our work directly with the closely related pattern-based Lift IR and compiler. We demonstrate that our language-oriented compiler design results in a more robust and predictable compiler that is extensible at various abstraction levels. Our experimental evaluation shows that this compiler design is able to generate high-performance GPU code.

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

Astroparticle physics is undergoing a profound transformation, due to a series of extraordinary new results, such as the discovery of high-energy cosmic neutrinos with IceCube, the direct detection of gravitational waves with LIGO and Virgo, and many others. This white paper is the result of a collaborative effort that involved hundreds of theoretical astroparticle physicists and cosmologists, under the coordination of the European Consortium for Astroparticle Theory (EuCAPT). Addressed to the whole astroparticle physics community, it explores upcoming theoretical opportunities and challenges for our field of research, with particular emphasis on the possible synergies among different subfields, and the prospects for solving the most fundamental open questions with multi-messenger observations., Comment: White paper of the European Consortium for Astroparticle Theory (EuCAPT). 135 authors, 400 endorsers, 133 pages, 1382 references