On the evolution of density perturbations in f(R) theories of gravity

Details On the evolution of density perturbations in f(R) theories of gravity On the evolution of density perturbations in f(R) theories of gravity

2008-02-21

arxiv.org/abs/0802.2999v2

Phys.Rev.D77:123515,2008

Astronomy and Astrophysics

Astrophysics

9 pages, 4 figures. New comments and references included. Final version to appear in Phys.Rev. D

Scientific paper

10.1103/PhysRevD.77.123515

In the context of $f(R)$ theories of gravity, we study the evolution of scalar cosmological perturbations in the metric formalism. Using a completely general procedure, we find the exact fourth-order differential equation for the matter density perturbations in the longitudinal gauge. In the case of sub-Hubble modes, the expression reduces to a second-order equation which 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 functions adequately describing the present phase of accelerated expansion and satisfying local gravity tests, it provides a correct description for the evolution of perturbations.

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