Scalar perturbations in cosmological $f(R)$ models: the cosmic screening approach

TL;DR

This paper develops a relativistic framework for analyzing scalar cosmological perturbations in nonlinear $f(R)$ gravity models, applicable across all scales under certain approximation conditions, and considers both discrete and continuous matter sources.

Contribution

It provides a full relativistic first-order perturbation theory for arbitrary nonlinear $f(R)$ models using the cosmic screening approach, simplifying the system to two master equations.

Findings

Scalar potentials are governed by two master equations.

The equations are valid at all spatial scales under the $rac{ ext{delta} R}{ar R} \,\ll 1$ approximation.

The approach applies to both point-like and continuous matter distributions.

Abstract

We investigate cosmological perturbations for nonlinear $f(R)$ models within the cosmic screening approach. Matter is considered both in the form of a set of discrete point-like massive bodies and in the form of a continuous pressureless perfect fluid. We perform full relativistic analysis of the first-order theory of scalar perturbations for arbitrary nonlinear $f(R)$ models and demonstrate that scalar potentials $\Phi(t,\mathbf{r})$ and $\Psi(t,\mathbf{r})$ are determined by a system of only two master equations. Our equations are applicable at all spatial scales as long as the approximation $\delta R/\bar R \ll 1$ (which is usually assumed in studies devoted to cosmological perturbations in $f(R)$ models) works.