Structure growth in f(R) theories of gravity with a dust equation of state

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 perturbations are derived using the covariant and gauge invariant approach and applied to two simple, yet widely studied f(R) gravity models. This analysis differs from existing analysis by the fact that the full fourth-order equations are studied. The equations are integrated without the implementation of the usual approximations which inevitably lead to a set of second-order equations. The structure of the general fourth-order perturbation equations and the analysis of scalar perturbations lead to the identification of interesting features in the matter power spectrum within fourth-order gravity. The fact that such features exist even in the case of such simple background models indicates the need for further detailed investigation within the context of more realistic scenarios.