A cosmology where GM = tc^3 is driven toward the stable density. The difference is made up by you and I, the matter we are made of. When the Universe is "underweight," quantum mechanics predicts that matter will appear via pair production. As we saw in the last post, the amount of this matter is the difference between $\rho$i and $\rho$f, or 4.507034%. This unique prediction is precisely confirmed by the Wilkinson Microwave Anistropy Probe.
In their paper on Time-Varying Speed of Light Albrecht and Maguiejo do not solve the flatness question, but suggest that a varying-c cosmology may someday answer it. Once this paper was published, Albrecht and Maguiejo discovered to their consternation that John Moffat had published a similar paper years earlier. They were all preceded by Thomson (Lord Kelvin) in 1874, so changing c is an old idea. Only in the 20th century, along with communism and fascism, did fixed c become dogma.
From their paper we can use Albrecht and Maguiejo's equation (10). Here R (not a) is scale and e is the deviation from critical density.
e = $\Omega$ - 1
edot = (1 + e)e(Rdot/R)(1 + 3w) + 2(cdot/c)e
Now we have w = 0,
From R=ct and GM=tc^3 we get:
(Rdot/R) = (2/3t) and (cdot/c) = (-1/3t)
edot = (1 + e)e(2/3t)(1 + 3w) + 2(-1/3t)e
edot = e^2 (2/3t)
Is it not reassuring that the other terms cancel? When t is low e is large and a large edot drives density toward a critical value. Today, when t is billions of years and e is very nearly zero, little mass is being created. Just as scale R began in a Bang and has been slowing since, the amount of mass creation has also been slowing and is now nearly zero.
Despite success, some people will act as if this isn't a Theory. It is painful to say that new ideas take time for others to figure out. Papers where c varies (including Albrecht and Maguiejo's) face great difficulties in publishing. Arthur Eddington joked in the 1920's that only 3 people understood Relativity, though he couldn't think of the third one! In the 21st century, we are on the way to solving "flatness" and other problems.