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