On the Newtonian limit of Generalized Modified Gravity Models

TL;DR

This paper investigates the Newtonian limit of modified gravity models with inverse curvature terms, showing that adding certain invariants can recover acceptable solar system behavior while still modifying gravity at galactic scales.

Contribution

It demonstrates that including inverse curvature invariants that do not vanish for Schwarzschild geometry can reconcile modified gravity models with solar system tests.

Findings

Acceptable Newtonian limit achieved with added curvature invariants.

Gravity modifications occur at large astrophysical distances.

First correction to Newtonian potential computed for general models.

Abstract

We consider the Newtonian limit of modified theories of gravity that include inverse powers of the curvature in the action in order to explain the cosmic acceleration. It has been shown that the simplest models of this kind are in conflict with observations at the solar system level. In this letter we point out that when one adds to the action inverse powers of curvature invariants that do not vanish for the Schwarzschild geometry one generically recovers an acceptable Newtonian limit at small distances. Gravity is however modified at large distances. We compute the first correction to the Newtonian potential in a quite general class of models. The characteristic distance entering in these modifications is of the order of 10pc for the Sun and of the order of 10^2 kpc for a galaxy.