🚀 go-pugleaf

  In reaction to my suggestion that, if anything, Newton predicts
a universe that expands with constant rate, Ted and Dave Ring
replied by saying that Newton did not necessarily make sense in
this situation. I agree. So we all seem to agree that 
`slow-down of expansion-rate due to mutual attraction' is falsely
appealing to Newtonian intuition.

My second point was that Einstein's theory predicts a universe
with constant expansion-rate if one `discretesizes' the
stress-energy tensor.

Dave Ring says that this is false because the global behaviour
of the universe is stable with respect to density-fluctuations.
I guess you are talking here about density-fluctuations of the
`perfect fluid'. What I had in mind was the following.

Idealize all matter to be concentrated in various discrete
points of the Friedmann spatial universe. Subsequently, regard
the stress-energy tensor as being zero outside the worlcurves
of these discrete matter-occupied points (and being something
irrelevant on the worldcurves). Thus the stress-energy tensor
is a `delta-tensor' d.

It is a straightforward exercise to check that Einstein's equation
G(g) = d (where g is a Friedmann-metric) has as solutions only
a static euclidean universe, or a hyperbolic universe that is 
either shrinking or expanding with constant rate.

The idealization seems not unreasonable in view of the following:
In a boundlessly expanding universe, call two massive objects
(particles) related if the round-trip time of radar-signals
between them remains bounded when time goes to infinity.
This relation is trivially seen to be an equivalence-relation.
Call the equivalence-classes *matter-systems*.

Because the universe expands forever boundlessly, there will be
more than one matter-system, two of those will recede with
ongoing time, and the Friedmann-spatial size of each will tend
to zero as time goes on.
Homogeneity implies that such a system converges (in the
Friedmann-spatial sense) to a comoving point. Call this point
the *home-point* of the matter-system.

In case of a `perfect fluid', each matter-system consists of
exactly one fluid particle, coinciding with its home-point.
In reality, a matter-system consists of a group of galaxies.

In any case, when one asks for the global structure of the 
universe, one asks for the mutual behaviour of the home-points.
Hence it seems o.k. to idealize matter to be concentrated in
home-points.

marc van loo.