Constraining Newtonian stellar configurations in f(R) theories of gravity

TL;DR

This paper analyzes metric f(R) gravity theories for stellar configurations, showing most cannot explain dark energy without conflicting with solar system tests, and provides first-order corrections to PPN parameters.

Contribution

It systematically solves f(R) field equations in a perturbative manner and demonstrates that many f(R) models predict PPN parameters incompatible with observations.

Findings

f(R) theories generally predict b3_{PPN}=1/2 in the solar system

First-order corrections to b3_{PPN} are negligible

Most f(R) models cannot explain dark energy without conflicting with solar system tests

Abstract

We consider general metric $f(R)$ theories of gravity by solving the field equations in the presence of a spherical static mass distribution by analytical perturbative means. Expanding the field equations systematically in $\cO(G)$, we solve the resulting set of equations and show that $f(R)$ theories which attempt to solve the dark energy problem very generally lead to $\gamma_{PPN}=1/2$ in the solar system. This excludes a large class of theories as possible explanations of dark energy. We also present the first order correction to $\gamma_{PPN}$ and show that it cannot have a significant effect.