In article , Ulf Torkelsson
wrote:

The formula you gave, GM/(c^2 r), would give hints on how big a
cosmological glob might become, as it should set a limit as GR forces grow
strong.

This is rather the length scale at which the curvature of space-time
becomes significant. If we use the critical density of the universe 1.88e-26
kg/m3, then this lenght scale becomes of order
r = (c^2/G rho)^(1/2) = 3e26 m = 1e10 ly
which is about the size of the observable universe.

There is one interesting consequence of this observation:

Suppose, for a start that the universe is made up by a series of globs,
each limited in size by the GR estimate GM/(c^2 r). Then this formula
would also act on the globs attracting to each other. It means that no
matter what the glob density is, the universe cannot be homogenous.

So this perhaps suggest that in such a case there should be another force
"levity" that counteracts gravity. This might be a an Einstein
cosmological constant or something or some other force. But this force
should be so that in the very large of the universe, the estimate GM/(c^2
r) is properly counteracted.

The interesting thing is that one ends up on a similar picture if one want
to explain the expansion of lit matter, if one wants to settle for an
older universe that is not created merely by a Big Bang.

I find this reasoning interesting, because I felt formerly sceptical over
the idea that GR should be augmented with some cosmological constant or
"levity" force. But perhaps this should be so.

Hans Aberg