A general framework to test gravity using galaxy clusters II: A universal model for the halo concentration in $f(R)$ gravity

Understand

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 $p_2\equiv1.5\log_{10}\left[|{\bar{f}_R(z)}|/(1+z)\right]+21.64$ 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 $z\leq3$, nearly 7 orders of magnitude in $M/10^{p_2}$ and five decades in halo mass.