The Parameterised 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®. We restrict ourselves to theories that admit Minkowski space as a suitable background, and perform a perturbative expansion in the manner prescribed by the parameterised 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 distinguished these theories from general relativity at the post-Newtonian level.