Dynamical Mechanism for Varying Light Velocity as a Solution to   Cosmological Problems
  A dynamical model for varying light velocity in cosmology is developed, based on the idea that there are two metrics in spacetime. One metric $g_{\mu\nu}$ describes the standard gravitational vacuum, and the other ${\hat g}_{\mu\nu} =g_{\mu\nu}+\beta\psi_\mu\psi_\nu$ describes the geometry through which matter fields propagate. Matter propagating causally with respect to $\hat{g}_{\mu\nu}$ can provide acausal contributions to the matter stress-energy tensor in the field equations for $g_{\mu\nu}$, which, as we explicitly demonstrate with perfect fluid and scalar field matter models, provides a mechanism for the solution of the horizon, flatness and magnetic monopole problems in an FRW universe. The field equations also provide a ``graceful exit'' to the inflationary epoch since below an energy scale (related to the mass of $\psi_\mu$) we recover exactly the standard FRW field equations. 
M. A. Clayton and J. W. Moffat