This paper presents a compelling argument for the physical light speed in the homogeneous and isotropic Friedman-Lemaitre-Robertson-Walker (FLRW) universe to vary with the cosmic time coordinate t of FLRW. It will be variable when the radial co-moving differential coordinate of FLRW is interpreted as physical and therefor transformable by a Lorentz transform locally to differentials of stationary physical coordinates. Because the FLRW differential radial distance has a time varying coefficient a(t), in the limit of a zero radial distance the light speed c(t) becomes time varying, proportional to the square root of the derivative of a(t) Since we assume homogeneity of space, this derived c(t) is the physical light speed for all events in the FLRW universe. This impacts the interpretation of astronomical observations of distant phenomena that are sensitive to light speed. A transform from FLRW is shown to have a physical radius out to all radial events in the visible universe. This shows a finite horizon beyond which there are no galaxies and no space. The general relativity (GR) field equation to determine a(t) and c(t) is maintained by using a variable gravitational constant and rest mass that keeps constant the gravitational and particle rest energies. This keeps constant the proportionality constant between the GR tensors of the field equation and conserves the stress-energy tensor of the ideal fluid used in the FLRW GR field equation. In the same way all of special and general relativity can be extended to include a variable light speed.
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