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

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 Rn 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 Mearos effect. (paper)