Chameleonf(R)gravity in the virialized cluster

Abstract

Current constraints on $f(R)$ gravity from the large-scale structure are at the verge of penetrating into a region where the modified forces become nonlinearly suppressed. For a consistent treatment of observables at these scales, we study cluster quantities produced in chameleon and linearized Hu-Sawicki $f(R)$ gravity dark matter $N$-body simulations. We find that the standard Navarro-Frenk-White halo density profile and the radial power law for the pseudo-phase-space density provide equally good fits for $f(R)$ clusters as they do in the Newtonian scenario. We give qualitative arguments for why this should be the case. For practical applications, we derive analytic relations, e.g., for the $f(R)$ scalar field, the gravitational potential, and the velocity dispersion as seen within the virialized clusters. These functions are based on three degrees of freedom fitted to simulations, i.e., the characteristic density, scale, and velocity dispersion. We further analyze predictions for these fitting parameters from the gravitational collapse and the Jeans equation, which are found to agree well with the simulations. Our analytic results can be used to consistently constrain chameleon $f(R)$ gravity with future observations on virialized cluster scales without the necessity of running a large number of simulations.