Cosmological density perturbations in modified gravity theories

TL;DR

This paper investigates the evolution of density perturbations in f(R) modified gravity theories, highlighting when common approximations are valid and providing a more general framework for understanding cosmological perturbations.

Contribution

It derives a general second-order differential equation for matter perturbations in f(R) theories, clarifying the validity of the quasi-static approximation.

Findings

Quasi-static approximation is not always justified in f(R) models.

For models explaining accelerated expansion and passing local tests, the approximation is valid.

The exact perturbation equation reduces to a simpler form for sub-Hubble modes.

Abstract

In the context of f(R) theories of gravity, we study the cosmological evolution of scalar perturbations by using a completely general procedure. We find that the exact fourth-order differential equation for the matter density perturbations in the longitudinal gauge, reduces to a second-order equation for sub-Hubble modes. This simplification is compared with the standard (quasi-static) equation used in the literature. We show that for general f(R) functions the quasi-static approximation is not justified. However for those f(R) adequately describing the present phase of accelerated expansion and satisfying local gravity tests, it does give a correct description for the evolution of perturbations.