Spherical collapse and halo mass function in f(R) theories

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 non-linear fluid equations, making the minimal simplifying assumptions that the metric potentials and scalar field remain quasi-static 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 delta_c as a function of collapse redshift, mass of the overdensity and f_{R0}, the background scalar field value at z=0. By extending delta_c into 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.