A general framework to test gravity using galaxy clusters II: A universal model for the halo concentration in $f(R)$ gravity. (arXiv:1901.06392v1 [astro-ph.CO])

<a href="http://arxiv.org/find/astro-ph/1/au:+Mitchell_M/0/1/0/all/0/1">Myles A. Mitchell</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Arnold_C/0/1/0/all/0/1">Christian Arnold</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+He_J/0/1/0/all/0/1">Jian-hua He</a> (2,1), <a href="http://arxiv.org/find/astro-ph/1/au:+Li_B/0/1/0/all/0/1">Baojiu Li</a> (1) ((1) ICC, Durham University, (2) Nanjing University)

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 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.

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