On the Newtonian Limit in Gravity Models with Inverse Powers of R

TL;DR

This paper investigates the Newtonian limit in nonlinear gravity models with inverse powers of Ricci scalar, proposing conditions for correct limits and introducing two specific models with particular second derivatives.

Contribution

It provides a detailed analysis of the Newtonian limit in inverse power gravity models and introduces two new models with specific properties of the second derivative of f(R).

Findings

Correct Newtonian limit requires |f(R_0)f''(R_0)|<< 1.

Expansion around maximally symmetric backgrounds is valid.

Two models with f''(R_0)=0 are proposed.

Abstract

I reconsider the problem of the Newtonian limit in nonlinear gravity models in the light of recently proposed models with inverse powers of the Ricci scalar. Expansion around a maximally symmetric local background with positive curvature scalar R_0 gives the correct Newtonian limit on length scales << R_0^{-1/2} if the gravitational Lagrangian f(R) satisfies |f(R_0)f''(R_0)|<< 1. I propose two models with f''(R_0)=0.