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

TL;DR

This paper models spherical collapse in f(R) gravity, deriving a new critical density threshold and halo mass function to compare modified gravity predictions with dark matter halo observations.

Contribution

It introduces a novel evolution approach for collapse equations in f(R) models and provides a fitting function for the collapse threshold as a function of key parameters.

Findings

Collapse threshold depends on initial conditions and model parameters.

Developed a realistic mass function for f(R) models using excursion set theory.

Validated the mass function against Monte Carlo simulations.

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 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.