Gravitational potential in Palatini formulation of modified gravity

TL;DR

This paper derives the gravitational potential in Palatini-modified gravity models of the L(R) type, showing they recover Newtonian gravity with minimal deviations, thus aligning with experimental tests.

Contribution

It provides the first derivation of the gravitational potential in Palatini L(R) gravity models that admit de Sitter solutions, confirming their consistency with weak-field tests.

Findings

Newtonian limit is always recovered in these models.

Deviations from General Relativity are very small for slow-moving sources.

Models admit de Sitter vacuum solutions.

Abstract

General Relativity has so far passed almost all the ground-based and solar-system experiments. Any reasonable extended gravity models should consistently reduce to it at least in the weak field approximation. In this work we derive the gravitational potential for the Palatini formulation of the modified gravity of the L(R) type which admits a de Sitter vacuum solution. We conclude that the Newtonian limit is always obtained in those class of models and the deviations from General Relativity is very small for a slowly moving source.