Constraints on fourth order generalized f(R) gravity

Details Constraints on fourth order generalized f(R) gravity Constraints on fourth order generalized f(R) gravity

2011-08-08

arxiv.org/abs/1108.1665v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, no figures

Scientific paper

A fourth order generalized f(R) gravity theory (FOG) is considered with the Einstein-Hilbert action $R+aR^{2}+bR_{\mu \nu}R^{\mu \nu},$ $R_{\mu \nu}$ being Ricci\'{}s tensor and R the curvature scalar. The field equations are applied to spherical bodies where Newtonian gravity is a good approximation. The result is that for $0\leq a\sim -b<>R^{2}$ the gravitational field near the body is zero but at distances greater than $\sqrt{a}\sim \sqrt{-b}$ the field is practically Newtonian. From the comparison with laboratory experiments I conclude that $\sqrt{a}$ and $\sqrt{-b}$ should be smaller than a few millimeters, which excludes any relevant effect of FOG on stars, galaxies or cosmology.

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