The evolution of density perturbations in f(R) 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.

21 pages, 2 figures, typos corrected, submitted to PRD

References in corpus (4)

• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• The Newtonian Limit of F(R) gravity
• The behavior of $f(R)$ gravity in the solar system, galaxies and clusters

Cited by in corpus (10)

• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Dark matter as a geometric effect in f(R) gravity
• Thin accretion disks in f(R) modified gravity models
• On the evolution of density perturbations in f(R) theories of gravity
• On the Stability of a class of Modified Gravitational Models
• Dark energy, inflation and dark matter from modified F(R) gravity
• The viability of theories with matter coupled to the Ricci scalar
• The Existence of Einstein Static Universes and their Stability in Fourth order Theories of Gravity
• Cosmological dynamics of exponential gravity