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Register a new userA general framework to test gravity using galaxy clusters V: A self-consistent pipeline for unbiased constraints of $f(R)$ gravity
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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.
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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 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.
The abundance of massive galaxy clusters is a powerful probe of departures from General Relativity (GR) on cosmic scales. Despite current stringent constraints placed by stellar and galactic tests, on larger scales alternative theories of gravity such as $f(R)$ can still work as effective theories. Here we present constraints on two popular models of $f(R)$, Hu-Sawicki and designer, derived from a fully self-consistent analysis of current samples of X-ray selected clusters and accounting for all the covariances between cosmological and astrophysical parameters. Using cluster number counts in combination with recent data from the cosmic microwave background (CMB) and the CMB lensing potential generated by large scale structures, as well as with other cosmological constraints on the background expansion history and its mean matter density, we obtain the upper bounds $log_{10}|f_{R0}| < 4.79$ and $log_{10}B_0 < 3.75$ at the 95.4 per cent confidence level, for the Hu-Sawicki (with $n=1$) and designer models, respectively. The robustness of our results derives from high quality cluster growth data for the most massive clusters known out to redshifts $z sim 0.5$, a tight control of systematic uncertainties including an accurate and precise mass calibration from weak gravitational lensing data, and the use of the full shape of the halo mass function over the mass range of our data.
We present an analysis of galaxy-galaxy weak gravitational lensing (GGL) in chameleon $f(R)$ gravity - a leading candidate of non-standard gravity models. For the analysis we have created mock galaxy catalogues based on dark matter haloes from two sets of numerical simulations, using a halo occupation distribution (HOD) prescription which allows a redshift dependence of galaxy number density. To make a fairer comparison between the $f(R)$ and $Lambda$CDM models, their HOD parameters are tuned so that the galaxy two-point correlation functions in real space (and therefore the projected two-point correlation functions) match. While the $f(R)$ model predicts an enhancement of the convergence power spectrum by up to $sim30%$ compared to the standard $Lambda$CDM model with the same parameters, the maximum enhancement of GGL is only half as large and less than 5% on separations above $sim1$-$2h^{-1}$Mpc, because the latter is a cross correlation of shear (or matter, which is more strongly affected by modified gravity) and galaxy (which is weakly affected given the good match between galaxy auto correlations in the two models) fields. We also study the possibility of reconstructing the matter power spectrum by combination of GGL and galaxy clustering in $f(R)$ gravity. We find that the galaxy-matter cross correlation coefficient remains at unity down to $sim2$-$3h^{-1}$Mpc at relevant redshifts even in $f(R)$ gravity, indicating joint analysis of GGL and galaxy clustering can be a powerful probe of matter density fluctuations in chameleon gravity. The scale dependence of the model differences in their predictions of GGL can potentially allow to break the degeneracy between $f(R)$ gravity and other cosmological parameters such as $Omega_m$ and $sigma_8$.
We consider $f(R)$ gravity theories which unify $R^n$ inflation and dark energy models. First, from the final Planck data of the cosmic microwave background, we obtain a condition, $1.977 < n < 2.003$. Next, under this constraint, we investigate local-gravity tests for three models. We find that the $R^n$ term can dominate over the dark energy term even at the Earths curvature scale, contrary to intuition; however, the $R^n$ term does not relax or tighten the constraints on the three models.
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