Testing the solar-system $γ_{PPN}$ constraint for $f(R)$ gravity around stationary spherically symmetric polytropes

Details Testing the solar-system $γ_{PPN}$ constraint for $f(R)$ gravity around stationary spherically symmetric polytropes Testing the solar-system $γ_{PPN}$ constraint for $f(R)$ gravity around stationary spherically symmetric polytropes

2011-10-31

arxiv.org/abs/1110.6711v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

8 pages, 3 figures

Scientific paper

As often stated, a class of $f(R)$ gravity models seem to obtain $\Lambda$CDM behavior for high red-shifts, and general relativistic behavior locally at high curvatures. In this paper, we study numerically sun-like configurations for one such proposed model, namely Hu-Sawicki $f(R)$ model having the chameleon property. Chameleon gravity theories are stated to reproduce general relativistic behavior within high curvature regime. Therefore stationary spherically symmetric configurations of $f(R)$ gravity with polytropic equation of state and regular metrics at the origin have been studied numerically and compared with general relativistic Eddington polytropes. To determine the metric deviation from relativistic Schwarzschild-de Sitter solution, post-Newtonian parametrization is used around the $f(R)$ polytropes. Since, Birkhoff's theorem does not need to hold within a modified gravity theory, the solution outside may be different. We find that although Schwarzchildian space-times can be produced with this model, they demand fine-tuning.

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