Asymptotically Schwarzschild solutions in f (R) extension of general relativity

We address the question of how to build a class of f(R) extensions of General Relativity which are compatible with solar system experiments, without making any preliminary assumption on the properties of f. The aim is reached by perturbatively solving the modified Einstein equations around a Schwarzschild background and retrieving a posteriori the corresponding f(R). This turns out to be non analytical in R=0 and should be intended as the leading correction to the Einstein-Hilbert action in the low curvature limit. The parameters characterizing the f(R) class are then set by constraining the corrections to four different local tests with the observations. The result is a class of f(R) theories built up from a purely bottom-up approach and compatible with the local tests. At a more general level, this result can help constraining exact f(R) models working in Cosmology, since it provides the correct local limit. Further developments and possible extensions of the approach to Cosmology are also discussed.