  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.
