Fourth order gravity and experimental constraints on Eddington parameters

PPN-limit of higher order theories of gravity represents a still controversial matter of debate and no definitive answer has been provided, up to now, about this issue. By exploiting the analogy between scalar-tensor and fourth-order theories of gravity, one can generalize the PPN-limit formulation. By using the definition of the PPN-parameters $\gamma$ and $\beta$ in term of the $f(R)$ derivatives, we show that a family of third-order polynomial theories, in the Ricci scalar $R$, turns out to be compatible with the PPN-limit and the deviation from General Relativity theoretically predicted agree with experimental data.