Axion homeopathy: screening dilaton interactions

Cosmologically active Brans-Dicke (or dilaton) scalar fields are generically ruled out by solar system tests of gravity unless their couplings to ordinary matter are much suppressed relative to gravitational strength, and this is a major hindrance when building realistic models of light dilatons coupled to matter. We propose a new mechanism for evading such bounds if matter also couples to a light axion, that exploits nonlinear target-space curvature interactions to qualitatively change how the fields respond to a gravitating source. We find that dilaton-matter couplings that would be excluded in the absence of an axion can become acceptable given an additional small axion-matter coupling, and this is possible because the axion-dilaton interactions end up converting the would-be dilaton profile into an axion profile. The trajectories of matter test bodies are then controlled by the much weaker axion-matter couplings and can easily be small enough to escape detection. We call this mechanism Axion Homeopathy because the evasion of the dilaton-coupling bounds persists for extremely small axion couplings provided only that they are nonzero. We explore the mechanism using axio-dilaton equations that are $SL(2,\mathbb{R})$ invariant (as often appear in string compactifications), since for these the general solutions exterior to a spherically symmetric source can be found analytically. We use this solution to compute the relevant PPN parameter, $\gamma_\PPN $, and verify that $\gamma_\PPN - 1$ can be much smaller than it would have been in the absence of axion-matter couplings and can therefore evade the experimental bounds.