Post-Newtonian Parameters from Alternative Theories of Gravity

TL;DR

This paper develops a theoretical framework within the Palatini formalism to test alternative gravity theories at solar system and galactic scales, deriving Post-Newtonian corrections consistent with observations.

Contribution

It introduces a method to derive Post-Newtonian parameters from alternative gravity theories in the Palatini formalism, aligning theoretical predictions with experimental data.

Findings

Exact vacuum solutions with corrections to GR

Approximate matter solutions with phenomenological parameters

Post-Newtonian deviations consistent with solar system tests

Abstract

Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini formalism) to test these theories at the solar system level and possibly at the galactic scales. We exactly solve field equations in vacuum and find the corresponding corrections to the standard general relativistic gravitational field. On the other hand, approximate solutions are found in matter cases starting from a Lagrangian which depends on a phenomenological parameter. Both in the vacuum case and in the matter case the deviations from General Relativity are controlled by parameters that provide the Post-Newtonian corrections which prove to be in good agreement with solar system experiments.