Constraints on fourth order generalized f(R) gravity

TL;DR

This paper investigates a fourth order generalized f(R) gravity theory, deriving constraints on its parameters based on gravitational behavior near spherical bodies and laboratory experiments, limiting its cosmological relevance.

Contribution

It provides new constraints on the parameters of fourth order generalized f(R) gravity by analyzing gravitational fields around spherical bodies and comparing with experimental data.

Findings

Gravitational field contains two Yukawa terms under certain parameter conditions.

Parameters must be smaller than a few millimeters based on laboratory experiments.

Relevance of the theory to stars, galaxies, or cosmology is excluded due to parameter constraints.

Abstract

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 $0\leq a\sim -b<<R^{2}$, $R$ being the body radius, the gravitational field outside the body contains two Yukawas, one attractive and the other one repulsive, in addition to the Newtonian term. For $a\sim -b>>R^{2}$ 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.