Scalar perturbations in cosmological f(R) models: the cosmic screening approach

Abstract

Abstract 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 $${\varPhi }(t,{\mathbf {r}})$$ Φ(t,r) and $${\varPsi }(t,{\mathbf {r}})$$ 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 $$\delta R/{\bar{R}} \ll 1$$ δR/R¯≪1 (which is usually assumed in studies devoted to cosmological perturbations in f(R) models) works.