`:::I'm glad you're OK with the edit, Nodem.  I didn't mean to offend by calling it a ``numerical coincidence.`` However that's the only reason I can think of for the calculation giving anywhere close to the right answer, except during radiation domination (which anyway is a poor approximation to our Universe at z < 10,000 or so).    :::It's possible that there's a principle behind it, but it seems that the principle must be false, or at least in severe conflict with observations.  As explained above, the essential reason is that it gives a time-temperature relation, and thus a time-scale factor relation, that would  :::* imply the universe is decelerating (since a(t) ~ t1/2) in conflict with SNIa observations, :::* disagree with observations of structure formation, which need a matter dominated epoch a(t) ~ t2/3 followed by dark energy domination, :::* be in conflict with the cosmic microwave background anisotropy, and especially the location of the first peak (since this essentially measures the angular diameter distance to the surface of last scattering, which depends on the behavior of the scale factor since then), :::* require us to replace the Friedmann equations and thus Einstein gravity.  In fact, since the radiation density is extremely tiny today, to get a(t) ~ t1/2 matter could not gravitate at all  definitely in conflict with observation.  :::All of this is pretty standard stuff, these arguments can be found on various Wikipedia pages (as well as in the scientific litertature and textbooks on cosmology).  If you want to talk further but don't want to do it here, you're welcome to post to my .  That way others can benefit from/contribute to the discussion if they wish.    `