Galileon forces in the Solar System

We consider the challenging problem of obtaining an analytic understanding of realistic astrophysical dynamics in the presence of a Vainshtein screened fifth force arising from infrared modifications of general relativity. In particular, we attempt to solve-within the most general flat spacetime Galileon model-the scalar force law between well separated bodies located well within the Vainshtein radius of the Sun. To this end, we derive the exact static Green's function of the Galileon wave equation linearized about the background field generated by the Sun, for the minimal cubic and maximally quartic Galileon theories, and then introduce a method to compute the general leading order force law perturbatively away from these limits. We also show that the same nonlinearities which produce the Vainshtein screening effect present obstacles to an analytic calculation of the Galileon forces between closely bound systems within the Solar System, such as that of the Earth and Moon. Within the test mass approximation, we deduce that a large enough quartic Galileon interaction would suppress the effect on planetary perihelion precession below the level detectable by even the next-generation experiments.