Consistency of $f(R)$ gravity models around solar polytropes

Abstract

It is stated that a class of $f(R)$ gravity models seem to obtain $\Lambda$CDM behaviour for high redshifts and general relativistic behaviour locally at high curvatures. In the present paper, we numerically study polytropic configurations that resemble stars like young sun with Hu and Sawicki $f(R)$ gravity field equations and compare the spacetime at the boundary to the general relativistic counterpart. These polytropes are stationary spherically symmetric configurations and have regular metrics at the origin. Since Birkhoff's theorem does not apply for modified gravity, the solution outside may deviate from Schwarzschild-de Sitter spacetime. At the boundary, Post-Newtonian parametrization was used to determine how much the studied model deviates from the general relativistic $\Lambda$CDM model.