Laser Ranging Delay in the Bi-Metric Theory of Gravity

We introduce a linearized bi-metric theory of gravity with two metrics. The metric gαβ describes null hypersurfaces of the gravitational field while light moves on null hypersurfaces of the optical metric ḡαβ. Bi-metrism naturally arises in vector-tensor theories with matter being non-minimally coupled to gravity via long-range vector field. We derive explicit Lorentz-invariant solution for a light ray propagating in space-time of the bi-metric theory and disentangle relativistic effects associated with the existence of the two metrics. This anlysis may be valuable for future spaceborne laser missions ASTROD and LATOR dedicated to map various relativistic gravity parameters in the solar system to unparalleled degree of accuracy.