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, f¹(R) and f²(R), of the Ricci scalar curvature R: the former extends the usual linear term found in the Einstein–Hilbert Lagrangian, while the latter is multiplied by the matter Lagrangian density, thus introducing an explicit nonminimal coupling. Based upon a Taylor expansion around R=0 for both functions, we find that the metric around a spherical object is a perturbation of the weak-field Schwarzschild metric: the perturbation of the tt component of the metric tensor is shown to be a Newtonian plus Yukawa term, which can be constrained using the available experimental results. It is shown that this effect can be canceled or made arbitrarily small when the characteristic mass scales of the two functions are similar. 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