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 pressure-less 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 Phi (t, r) and psi (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 delta R/(R) over bar << 1 (which is usually assumed in studies devoted to cosmological perturbations in f (R) models) works.