The Parameterised Post-Newtonian Limit of Fourth-Order Theories of Gravity

TL;DR

This paper derives the full post-Newtonian limit of f(R) gravity theories, revealing additional potentials that could help distinguish these theories from general relativity through observations.

Contribution

It provides a comprehensive derivation of the post-Newtonian limit for f(R) theories, including new potentials not previously considered in standard analyses.

Findings

Extra potentials identified in the post-Newtonian expansion

Potential observational signatures to differentiate theories from GR

Framework applicable to theories with Minkowski background

Abstract

We determine the full post-Newtonian limit of theories of gravity that extend general relativity by replacing the Ricci scalar, R, in the generating Lagrangian by some analytic function, f(R). We restrict ourselves to theories that admit Minkowski space as a suitable background, and perform a perturbative expansion in the manner prescribed by the parameterised post-Newtonian formalism. Extra potentials are found to be present that are not accounted for in the usual treatment, and a discussion is provided on how they may be used to observationally distinguished these theories from general relativity at the post-Newtonian level.