$f(R)$ gravity: scalar perturbations in the late Universe

Understand

In this paper we study scalar perturbations of the metric 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, getting 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 $a$.