The 1/c expansion of nonminimally coupled curvature-matter gravity model and constraints from planetary precession

TL;DR

This paper investigates how a nonminimally coupled curvature-matter gravity model affects planetary precession, extending previous theoretical work to include higher-order corrections and assessing potential experimental constraints.

Contribution

It extends the theoretical framework of nonminimally coupled gravity models to include corrections up to order 1/c^4 and explores their implications for planetary precession.

Findings

Additional contributions from non-linear $f^1(R)$ and nonminimal coupling $f^2(R)$.

Exponential terms in the metric corrections that are not power series in 1/r.

Potential experimental constraints from planetary precession data.

Abstract

The effects of a nonminimally coupled curvature-matter model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. This work expands upon previous results, extending the framework developed there to compute corrections up to order $O(1/c^4)$ of the $00$ component of the metric tensor. It is shown that additional contributions arise due to both the non-linear form $f^1(R)$ and the nonminimal coupling $f^2(R)$, including exponential contributions that cannot be expressed as an expansion in powers of $1/r$. Some possible experimental implications are assessed with application to perihelion precession.