Mimicking general relativity in the Solar System

In order for a modified gravity model to be a candidate for cosmological dark energy, it has to pass stringent local gravity experiments. We find that a Brans-Dicke (BD) theory with well-defined second order corrections that include the Gauss-Bonnet term possesses this feature. We construct the generic second order theory that gives, to linear order, a BD metric solution for a pointlike mass source. We find that the Eddington parameter $\gamma$, heavily constrained by time delay experiments, can be arbitrarily close to the general relativity value of 1, with an arbitrary BD parameter ${\omega }_{\mathrm{BD}}$. We find the region where the solution is stable to small timelike perturbations.