  This paper presents a compelling argument for the physical light speed in the
Friedman-Lemaitre-Robertson-Walker (FLRW) universe to vary with the cosmic time
coordinate "t" of FLRW. It must be variable when the radial comoving
differential coordinates of FLRW is interpreted as physical and therefore
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), integration of the transformed differentials to
obtain stationary coordinates for a short radial distance requires the light
speed c(t) to be proportional to the square root of da/dt. Since we assume
homogeneity of space, this derived c(t) is the physical light speed on all
points of the FLRW universe. This impacts the interpretation of all
astronomical observations of distant phenomena that are sensitive to light
speed. A world transform from FLRW that has a Minkowski metric close to the
origin is shown to have a physical radius out to all points of the visible
universe. In order to obtain numerical values for c(t), the general relativity
(GR) field equation is extended by using a variable gravitational constant and
rest mass that keeps constant the gravitational and particle rest energies.
This also keeps constant the proportionality constant between the GR tensors of
the field equation and conserves the rest stress-energy tensor of the ideal
fluid used in the FLRW GR field equation. In the same way all of special and
general relativity is extended to include a variable light speed.
