The speed of light as a dependent cosmological parameter and the gravitational attenuation of distant matter

The coincidence between the square of the speed of light, c², and the Newtonian gravitational potential of the universe, suggests a dependence of the magnitude of c on cosmological parameters. Such a cosmological dependence is obtained by applying standard initial-value considerations of general relativity to the cosmological Robertson-Walker metric. Specifically, the time-time component of the cosmological metric is considered as a variable field on spatial foliations of the cosmological metric. A basic quantification emerges for c² in terms of the gravitational constant G, the cosmological matter density ρ, and the cosmological constant Λ, such that c²∼ ρG/Λ. The Newtonian result obtains from the non-linear elliptic equation for the case of a matter-only universe, but in that case, c is not independently quantified. The cosmological constant plays a crucial role, not only in providing a lengthscale that can be combined with the timescale of ρG to provide a cosmological velocity scale, but also in attenuating the gravitational effect of distant matter compared to a Newtonian calculation. Although variation of the speed of light is implied on cosmological time scales, there is no effect on the Friedmann equation, and conservation of energy is preserved.