All physical transforms from RW require the universe to have the same variable physical photon velocity
I have investigated what coordinate systems, other than the RobertsonWalker (RW) system, there might be to describe a homogeneous and isotropic universe that are physical close to the origin, i.e., covariant transforms from RW that there have a Minkowski metric. I show that all possible such systems must have the same variable photon velocity close to their origin, which is consistent with the RW system also having the same variable photon velocity. Implausible though it may seem, if the criteria for physicality are valid, it seems inescapable that this must represent the physical photon velocity c(t). The assumption of homogeneity makes it applicable to physical processes throughout the universe. I find that the analytic expression for it is c(t) = ah, the cosmic scale factor times the Hubble ratio in appropriate units. The existence of variability derives from the physicality criteria being applied to the transformed coordinates expanded from the origin out to the lowest order of the RW radial coordinate, and not to gravitational energy density, which determines only its magnitude. I show that there are covariant transforms which are physical over a large fraction of the universe’s space-time. The replacement of the RW time by a generalized time, for which the differential is c(t)dt, keeps invariant the Lorentz transform, the Minkowski metric and the Einstein field equation. These can then be used to preserve and extend all our physical laws. Other physical “constants” that depend on the photon velocity may also change. keywords: cosmology theory—distances and redshifts—elementary particlesvariable light velocity ∗Mailing address: 1000 Oak Hills Way, Salt Lake City, UT 84108. robcfletcher@comcast.net