Jumping from Metric f(R) to Scalar-Tensor Theories and the relations between their post-Newtonian Parameters

We review the dynamical equivalence between $f(R)$ gravity in the metric formalism and scalar-tensor gravity, and use this equivalence to deduce the post-Newtonian parameters $\gamma$ and $\beta$ for a $f(R)$ theory, obtaining a result that is different with respect to that known in the literature. Then, we obtain explicit expressions of these paremeters in terms of the mass of the scalar field (or, differently speaking, the mass of the additional scalar degree of freedom associated to a $f(R)$ theory) which can be used to constrain $f(R)$ gravity by means of current observations.