A Nonminimal Coupling Model and its Short-Range Solar System Impact

The objective of this work is to present the effects of a nonminimally coupled model of gravity on a Solar System short range regime. For this reason, this study is only valid when the cosmological contribution is considered irrelevant. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$, where the last one multiplies the matter Lagrangian. Using a Taylor expansion around $R=0$ for both functions $f^1(R)$ and $f^2(R)$, it was found that the metric around a spherical object is a perturbation of the weak-field Schwarzschild metric. The $tt$ component of the metric, a Newtonian plus a Yukawa perturbation term, is constrained using the available observational results. First it is shown that this effect is null when the characteristic mass scales of each function $f^1(R)$ and $f^2(R)$ are identical. Besides, the conclusion is that the nonminimal coupling only affects the Yukawa contribution strength and not its range and that the Starobinsky model for inflation is not experimentally constrained. Moreover, the geodetic precession effect, obtained also from the radial perturbation of the metric, reveals to be of no relevance for the constraints.