Parametrized post-Newtonian limit of fourth-order theories of gravity

We determine the full post-Newtonian limit of theories of gravity that extend general relativity by replacing the Ricci scalar, $R$, in the generating Lagrangian by some analytic function, $f(R)$. We restrict ourselves to theories that admit Minkowski space as a suitable background, and perform a perturbative expansion in the manner prescribed by the parametrized post-Newtonian formalism. Extra potentials are found to be present that are not accounted for in the usual treatment, and a discussion is provided on how they may be used to observationally distinguish these theories from general relativity at the post-Newtonian level.