A detailed analysis of structure growth in $f(R)$ theories of gravity

TL;DR

This paper analyzes scalar perturbations in $f(R)$ gravity models to identify unique signatures in the matter power spectrum, offering potential tests for these theories on cosmological scales.

Contribution

It derives the evolution equations for scalar perturbations in $f(R)$ gravity using a covariant approach and identifies distinctive features in the matter power spectrum.

Findings

Discovery of a characteristic signature in the matter power spectrum for $f(R)$ models

Derivation of general fourth order perturbation equations

Potential for new cosmological tests of $f(R)$ gravity

Abstract

We investigate the connection between dark energy and fourth order gravity by analyzing the behavior of scalar perturbations around a Friedmann-Robertson-Walker background. The evolution equations for scalar perturbation are derived using the covariant and gauge invariant approach and applied to two widely studied $f(R)$ gravity models. The structure of the general fourth order perturbation equations and the analysis of scalar perturbations lead to the discovery of a characteristic signature of fourth order gravity in the matter power spectrum, the details of which have not seen before in other works in this area. This could provide a crucial test for fourth order gravity on cosmological scales.