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

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.

21 pages, 7 figures

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• The solar system test for the general modified gravity theories
• Cassini and extra force constraints to nonminimally coupled gravity with screening mechanism
• Pressureless stationary solutions in a Newton-Yukawa gravity model
• Theories of gravity with nonminimal matter-curvature coupling and the de Sitter swampland conjectures
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