The evolution of density perturbations in f(R) gravity

TL;DR

This paper develops a rigorous covariant gauge-invariant framework for scalar perturbations in f(R) gravity, revealing unique growth behaviors of density perturbations even during accelerated expansion, unlike in standard GR.

Contribution

It provides the first exact solutions for scalar perturbations in R^n gravity, highlighting novel growth modes of density contrast during accelerated phases.

Findings

Existence of a persistent growing mode in density contrast for all n values.

Density perturbations behave differently in f(R) gravity compared to standard GR during acceleration.

Exact solutions are obtained for super-Hubble scales in R^n gravity.

Abstract

We give a rigorous and mathematically well defined presentation of the Covariant and Gauge Invariant theory of scalar perturbations of a Friedmann-Lemaitre-Robertson-Walker universe for Fourth Order Gravity, where the matter is described by a perfect fluid with a barotropic equation of state. The general perturbations equations are applied to a simple background solution of R^n gravity. We obtain exact solutions of the perturbations equations for scales much bigger than the Hubble radius. These solutions have a number of interesting features. In particular, we find that for all values of n there is always a growing mode for the density contrast, even if the universe undergoes an accelerated expansion. Such a behaviour does not occur in standard General Relativity, where as soon as Dark Energy dominates, the density contrast experiences an unrelenting decay. This peculiarity is sufficiently novel to warrant further investigation on fourth order gravity models.