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

Abstract

In this work, the effects of a nonminimally coupled model of gravity on a\nperturbed Minkowski metric are presented. The action functional of the model\ninvolves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$.\nBased upon a Taylor expansion around $R = 0$ for both functions $f^1(R)$ and\n$f^2(R)$, we find that the metric around a spherical object is a perturbation\nof the weak-field Schwarzschild metric: the time perturbation is shown to be a\nNewtonian plus Yukawa term, which can be constrained using the available\nexperimental results. We conclude that the Starobinsky model for inflation\ncomplemented with a generalized preheating mechanism is not experimentally\nconstrained by observations. The geodetic precession effects of the model are\nalso shown to be of no relevance for the constraints.\n