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Register a new userA general framework to test gravity using galaxy clusters IV: Cluster and halo properties in DGP gravity
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We study and model the properties of galaxy clusters in the normal-branch Dvali-Gabadadze-Porrati (nDGP) model of gravity, which is representative of a wide class of theories which exhibit the Vainshtein screening mechanism. Using the first cosmological simulations which incorporate both full baryonic physics and nDGP, we find that, despite being efficiently screened within clusters, the fifth force can raise the temperature of the intra-cluster gas, affecting the scaling relations between the cluster mass and three observable mass proxies: the gas temperature, the Compton $Y$-parameter of the Sunyaev-Zeldovich effect and the X-ray analogue of the $Y$-parameter. Therefore, unless properly accounted for, this could lead to biased measurements of the cluster mass in tests that make use of cluster observations, such as cluster number counts, to probe gravity. Using a suite of dark-matter-only simulations, which span a wide range of box sizes and resolutions, and which feature very different strengths of the fifth force, we also calibrate general fitting formulae which can reproduce the nDGP halo concentration at percent accuracy for $0leq zleq1$, and halo mass function with $lesssim3%$ accuracy at $0leq zleq1$ (increasing to $lesssim5%$ for $1leq zleq 2$), over a halo mass range spanning four orders of magnitude. Our model for the concentration can be used for converting between halo mass overdensities and predicting statistics such as the nonlinear matter power spectrum. The results of this work will form part of a framework for unbiased constraints of gravity using the data from ongoing and upcoming cluster surveys.
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We present a novel fitting formula for the halo concentration enhancement in chameleon $f(R)$ gravity relative to General Relativity (GR). The formula is derived by employing a large set of $N$-body simulations of the Hu-Sawicki $f(R)$ model which cover a wide range of model and cosmological parameters, resolutions and simulation box sizes. The complicated dependence of the concentration on halo mass $M$, redshift $z$, and the $f(R)$ and cosmological parameters can be combined into a simpler form that depends only on a rescaled mass $M/10^{p_2}$, with $p_2equiv1.5log_{10}left[|{bar{f}_R(z)}|/(1+z)right]+21.64$ and $bar{f}_R(z)$ the background scalar field at $z$, irrespective of the $f(R)$ model parameter. Our fitting formula can describe the concentration enhancement well for redshifts $zleq3$, nearly 7 orders of magnitude in $M/10^{p_2}$ and five decades in halo mass. This is part of a series of works which aims to provide a general framework for self-consistent and unbiased tests of gravity using present and upcoming galaxy cluster surveys. The fitting formula, which is the first quantitative model for the concentration enhancement due to chameleon type modified gravity, is an important part in this framework and will allow continuous exploration of the parameter space. It can also be used to model other statistics such as the matter power spectrum.
We present a Markov chain Monte Carlo pipeline that can be used for robust and unbiased constraints of $f(R)$ gravity using galaxy cluster number counts. This pipeline makes use of a detailed modelling of the halo mass function in $f(R)$ gravity, which is based on the spherical collapse model and calibrated by simulations, and fully accounts for the effects of the fifth force on the dynamical mass, the halo concentration and the observable-mass scaling relations. Using a set of mock cluster catalogues observed through the thermal Sunyaev-Zeldovich effect, we demonstrate that this pipeline, which constrains the present-day background scalar field $f_{R0}$, performs very well for both $Lambda$CDM and $f(R)$ fiducial cosmologies. We find that using an incomplete treatment of the scaling relation, which could deviate from the usual power-law behaviour in $f(R)$ gravity, can lead to imprecise and biased constraints. We also find that various degeneracies between the modified gravity, cosmological and scaling relation parameters can significantly affect the constraints, and show how this can be rectified by using tighter priors and better knowledge of the cosmological and scaling relation parameters. Our pipeline can be easily extended to other modified gravity models, to test gravity on large scales using galaxy cluster catalogues from ongoing and upcoming surveys.
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.
We propose a new cosmological test of gravity, by using the observed mass fraction of X-ray emitting gas in massive galaxy clusters. The cluster gas fraction, believed to be a fair sample of the average baryon fraction in the Universe, is a well-understood observable, which has previously mainly been used to constrain background cosmology. In some modified gravity models, such as $f(R)$ gravity, gas temperature in a massive cluster is determined by the effective mass of that cluster, which can be larger than its true mass. On the other hand, X-ray luminosity is determined by the true gas density, which in both modified gravity and $Lambda$CDM models depends mainly on $Omega_{rm b}/Omega_{rm m}$ and hence the true total cluster mass. As a result, the standard practice of combining gas temperatures and X-ray surface brightnesses of clusters to infer their gas fractions can, in modified gravity models, lead to a larger - in $f(R)$ gravity this can be $1/3$ larger - value of $Omega_{rm b}/Omega_{rm m}$ than that inferred from other observations such as the CMB. A quick calculation shows that the Hu-Sawicki $n=1$ $f(R)$ model with $|bar{f}_{R0}|=3sim5times10^{-5}$ is in tension with the gas fraction data of the 42 clusters analysed by Allen et al. (2008). We also discuss the implications for other modified gravity models.
Changes in the law of gravity have far-reaching implications for the formation and evolution of galaxy clusters, and appear as peculiar signatures in their mass-observable relations, structural properties, internal dynamics, and abundance. We review the outstanding progress made in recent years towards constraining deviations from General Relativity with galaxy clusters, and give an overview of the yet untapped information becoming accessible with forthcoming surveys that will map large portions of the sky in great detail and unprecedented depth.
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