http://arxiv.org/abs/1401.5410
In this paper, we study scalar perturbations of the metrics for nonlinear $f(R)$ models. We consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. We investigate the astrophysical approach in the case of Minkowski spacetime background and two cases in the cosmological approach: the large scalaron mass approximation and the quasi-static approximation, and get explicit expressions for scalar perturbations for both these cases. In the most interesting quasi-static approximation, the scalar perturbation functions depend on both the nonlinearity function $f(R)$ and the scale factor $a$. Hence, we can study the dynamical behavior of the inhomogeneities (e.g., galaxies and dwarf galaxies) including into the consideration their gravitational attraction and the cosmological expansion, and also taking into account the effects of the nonlinearity. Our investigation is valid for functions $f(R)$ which have stable de Sitter points in future with respect to the present time, that is typical for the most popular $f(R)$ models.
Wed, 22 Jan 14
12/66
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