Solar system constraints on Gauss–Bonnet mediated dark energy

Although the Gauss–Bonnet term is a topological invariant for general relativity, it couples naturally to a quintessence scalar field, modifying gravity at solar system scales. We determine the solar system constraints due to this term by evaluating the post-Newtonian metric for a distributional source. We find a mass-dependent, 1/ r 7 correction to the Newtonian potential, and also deviations from the Einstein gravity prediction for light-bending. We constrain the parameters of the theory using planetary orbits, the Cassini spacecraft data, and a laboratory test of Newton's law, always finding extremely tight bounds on the energy associated to the Gauss–Bonnet term. We discuss the relevance of these constraints to late-time cosmological acceleration.