Hans Aberg wrote:

In article , Ulf Torkelsson
wrote:
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.


In the last paragraph here you reason the same way as Einstein did
when he introduced his cosmological constant. Gravity is always
attractive, so in order to get a static universe he was forced to
introduce the cosmological constant to counteract gravity on large
distance scales. If you do not assume that the universe is static
the cosmological constant is no longer necessary, and we can for
instance get an expanding universe in which the expansion is
gradually slowing down due to the effect of gravity. If we keep
the cosmological constant, but allow the universe to change
over time, it turns out that the static solution is unstable, and any
perturbation will either cause it to contract or expand. The
interesting thing here is that the expansion can eventually become
exponential if we do have a cosmological constant.

Ulf Torkelsson

[Mod. note: quoted text trimmed -- mjh]