Spherical collapse and halo mass function inf(R)theories

Abstract

We compute the critical density of collapse for spherically symmetric overdensities in a class of $f(R)$ modified gravity models. For the first time we evolve the Einstein, scalar field and nonlinear fluid equations, making the minimal simplifying assumptions that the metric potentials and scalar field remain quasistatic throughout the collapse. Initially evolving a top-hat profile, we find that the density threshold for collapse depends significantly on the initial conditions imposed, specifically the choice of size and shape. By imposing ``natural'' initial conditions, we obtain a fitting function for the spherical collapse ${\ensuremath{\delta}}_{c}$ as a function of collapse redshift, mass of the overdensity and ${f}_{\mathrm{R}0}$, the background scalar field value at $z=0$. By extending ${\ensuremath{\delta}}_{c}$ into a drifting and diffusing barrier within the context of excursion set theory, we obtain a realistic mass function that might be used to confront this class of scalar-tensor models with observations of dark-matter halos. The proposed analytic formula for the halo mass function was tested against Monte Carlo random walks for a wide class of moving barriers and can therefore be applied to other modified gravity theories.