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Perturbation of the metric around a spherical body from a nonminimal coupling between matter and curvature

In this work, the effects of a nonminimally coupled 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 $R$. Based upon a Taylor expansion around $R = 0$ for both functions $f^1(R)$ and $f^2(R)$, we find that the metric around a spherical object is a perturbation of the weak-field Schwarzschild metric: the time perturbation is shown to be a Newtonian plus Yukawa term, which can be constrained using the available experimental results. We conclude that the Starobinsky model for inflation complemented with a generalized preheating mechanism is not experimentally constrained by observations. The geodetic precession effects of the model are also shown to be of no relevance for the constraints.