Post-Newtonian Parameters from Alternative Theories of Gravity

TL;DR

This paper addresses testing higher-order gravity theories of the form $L(R)$ within the Palatini formalism against solar-system data and cosmological considerations. It develops a theoretical framework where the independent connection induces a bi-metric structure and a structural equation $L'(R)R-2L(R)=\kappa\tau$, leading to generalized Einstein equations that reduce to Schwarzschild–de Sitter in vacuum with a PN-like parameter $\mu=c_i/4$. In linearized, matter-filled spacetimes, the authors derive PN corrections controlled by a scale parameter $\alpha$ in $L(R)=R+\alpha f(R)$, showing GR is recovered as $\alpha\to0$ and that deviations vanish at solar-system scales while potentially contributing at cosmological or galactic scales. The results support the viability of broad L(R) families under solar-system constraints and suggest a scale-dependent departure from GR manifesting mainly at large scales, with implications for future tests of gravity in cosmology and at galactic levels.

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.