Solar System Constraints on Gauss-Bonnet Mediated Dark Energy

TL;DR

This work investigates solar-system and laboratory constraints on gravity with a scalar field coupled to the Gauss-Bonnet invariant, deriving the leading post-Newtonian corrections for a distributional source and predicting a mass-dependent $1/r^7$ Gauss-Bonnet term alongside light-bending deviations. By connecting these corrections to observables, the authors extract stringent bounds on the coupling combination $\alpha\,\xi_1'$ and on the Gauss-Bonnet dark-energy fraction $\Omega_{GB}$ from planetary motions, the Cassini frequency shift, and a table-top experiment. The resulting limits, notably $|\Omega_{GB}| \lesssim 3.6\times10^{-32}$ from Cassini, imply that Gauss-Bonnet contributions to late-time acceleration must be highly suppressed locally, unless significant scale-dependent dynamics or screening mechanisms are at play. Overall, the paper highlights the tension between Gauss-Bonnet dark energy scenarios and precision solar-system tests, and outlines possible avenues (e.g., chameleon effects, differential couplings, or higher-order kinetic terms) to reconcile them.

Abstract

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.