Novel Screening with Two Bodies: Summing the ladder in disformal scalar-tensor theories

Abstract

When augmenting our cosmological models or gravitational theories with an additional light scalar field, any coupling between matter and this scalar can affect the orbital motion of binary systems. Ordinarily, the new force mediated by the scalar can be naturally the same order of magnitude as the usual gravitational force and therefore is tightly constrained. We show that a disformal coupling between the scalar and matter can lead to a novel screening mechanism in which these fifth forces are suppressed by several orders of magnitude at sufficiently small separations and large relative velocities (such as solar system scales). This is a result of resumming a class of ladder diagrams, which suppresses the propagation of scalar signals between the two bodies. Moreover, we are able to relate potential ambiguities in this resummation to non-perturbative effects (which are invisible to perturbation theory). As a result, solar system tests and future gravitational wave observations can now be used to place meaningful constraints on scalar-tensor theories with disformal couplings. We exemplify this using observational bounds on the precession of planetary orbits.

Half-solution to the two-body problem in General Relativity

“…The vertices are of two types: the bulk nonlinearities originating from the Einstein-Hilbert action, and the worldline couplings coming from the matter action describing the two point-particles. In this Letter, we point out that the introduction of two worldline parameters -or einbeins [24] -allows to drastically simplify the worldline couplings, leaving an action containing only a linear coupling of the graviton to the source (similar parametrization was already used for the two-body problem in the context of modified gravity [25]). The number of Feynman diagrams needed to evaluate the action at each perturbative order is thus greatly reduced, so that the only computational obstacle in the two-body problem is entirely contained in the Einstein-Hilbert action.…”