Post-Newtonian constraints on f(R) cosmologies in Palatini formalism

We compute the complete post-Newtonian limit of the Palatini form of f(R) gravities using a scalar-tensor representation. By comparing the predictions of these theories with laboratory and solar system experiments, we find a set of inequalities that any lagrangian f(R) must satisfy. The constraints imposed by those inequalities allow us to find explicit functions that bound from above and from below the possible nonlinear terms of the lagrangian. We conclude that the lagrangian f(R) must be almost linear in R and that nonlinear corrections that grow at low curvatures are incompatible with observations. This result shows that modifications of gravity at very low cosmic densities cannot be responsible for the observed cosmic speed-up.