"Variations in the speed of light"

More and more physicists are willing to consider that the speed of light may be changing, as predicted. From phys.org:

Physicists propose method to measure variations in the speed of light

"But in some alternative theories of cosmology, the speed of light is not actually constant, but varies throughout time and space."

The physicists from universities in Poland and Spain propose to use baryon acoustic oscillations, waves in the microwave background that can theoretically be detected and measured. Their pasper appears, behind a paywall, in Physical Review Letters:

Measuring the speed of light with baryon acoustic oscillations

The article in phys.org mentions a simple relationship: There is an angular diameter distance Da, which can be multiplied by the Hubble factor H to get the speed of light:

DaH = c

We can calculate Da, the maximum distance light has travelled from the time of highest redshift. M = R = t in Planck units, which in CGS units becomes: GM = tc^3 and R = ct

c(t) = (GM)^[1/3]t^[-1/3]

Da = \int c(t)dt = (3/2)(GM)^[1/3]t^[2/3] integrated from t = 0 (the Big Bang) to the present time.

Note that (GM)^[1/3]t^[-1/3] = c, so:

Da = (3/2)ct

Now we figure out the Hubble value H = Rdot/R

R(t) = ct = (GM)^[1/3]t^[2/3]

\Rdot(t) = (2/3)(GM)^[1/3]t^{-1/3]

H = \Rdot /R = (2/3t)

Putting it all together:

DaH = (3/2)ct(2/3t) = c

Matches perfectly, no? A simple cosmology of M = R = t fits the relation DaH = c. Why hasn't anyone noticed this before?