Constraints on a cubic Galileon disformally coupled to Standard Model matter

We consider a disformal coupling between Standard Model matter and a cubic Galileon scalar sector, assumed to be a relict of some other physics that solves the cosmological constant problem rather than a solution in its own right. This allows the energy density carried by the Galileon scalar to be sufficiently small that it evades stringent constraints from the integrated Sachs-Wolfe effect, which otherwise rules out the cubic Galileon theory. Although the model with disformal coupling does not exhibit Vainshtein screening, we show there is a cosmological `screening-like' phenomenon in which the energy density carried by the Galileon scalar is suppressed during matter domination when the quadratic and cubic Galileon operators are both relevant. We obtain the explicit 3+1 form of Maxwell's equations in the presence of the disformal coupling, and the wave equations that govern electromagnetic waves. The disformal coupling is known to generate a small mass that modifies their velocity of propagation. We use the WKB approximation to study electromagnetic waves in this theory and show that, despite remarkable recent constraints from the LIGO/Virgo observatories that restrict the difference in propagation velocity between electromagnetic and gravitational radiation to roughly 1 part in 1015, the disformal coupling is too weak to be constrained by events such as GW170817 or by the dispersion of electromagnetic radiation at different wavelengths.