Scalar perturbations in cosmological f(R) models. The cosmic screening approach

We investigate cosmological perturbations for nonlinear f(R) models within the cosmic screening approach. Matter is considered both in the form of a set of discrete point-like massive bodies and in the form of a continuous pressureless perfect fluid. We perform full relativistic analysis of the first-order theory of scalar perturbations for arbitrary nonlinear f(R) models and demonstrate that scalar potentials Φ(t, r) and Ψ(t, r) are determined by a system of only two master equations. Our equations are applicable at all spatial scales as long as the approximation δR/ anti R << 1 (which is usually assumed in studies devoted to cosmological perturbations in f(R) models) works. (orig.)