Covariant gauge-invariant perturbations in multifluid f (R) gravity

Abstract

We study the evolution of scalar cosmological perturbations in the 1 + 3 covariant gauge-invariant formalism for generic f(R) theories of gravity. Extending previous works, we give a complete set of equations describing the evolution of matter and curvature fluctuations for a multi-fluid cosmological medium. We then specialize to a radiation-dust fluid described by barotropic equations of state and solve the perturbation equations around a background solution of R^n gravity. In particular, we study exact solutions for scales much smaller and much larger than the Hubble radius and show that n > 2/3 in order to have a growth rate compatible with the Mészáros effect.