Re: expansion of the universe

[David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>]

Regarding Gary Turner's comment:

> > Current measurements indicate that the universe is probably not
> > closed.  Rather, it is "critical" or "open".  In either of these
> > cases, the universe has an infinite amount of space AND ALWAYS HAS
> > HAD AN INFINTE AMOUNT OF SPACE, no?
>
> No, not really. The universe is expanding at a finite rate and has been
> doing so for a finite time.

Ok so far (once we properly define the meaning of "at a finite rate"
to mean 'having a finite Hubble parameter').

> It is finitely big.

This claim is a non sequitur.

> After it has been
> expanding for an infinite amount of time, it will be infinitely big.

But it may *already be* infinitely big.  The argument above does not
decide the issue.

> If you fire a particle away from the Earth at greater than escape speed, it
> will continue to separate from the Earth forever - but in 10 years, it will
> not be an infinite distance away.

This has nothing to do with the cosmological issue at hand.

> Cosmologically, it is a little harder than this example because parts of
> the universe may be beyond our horizon.

Maybe even an infinite amount of it is beyond our horizon.

> They are so far away that light
> cannot have reached us, so cannot be observed.  For all intents and
> purposes, they may as well be an infinite distance away because they cannot
> possibly affect us at the moment.

This is fair.  And it also illustrates the practical difficulty of
actually deciding the issue based on observation.

> However, they are not.

This is an unsubstantiated claim.

> It is just the
> constraint of finite transmission speeds over extremely large (but finite)
> distances.

But it doesn't answer the question of whether or not the universe is
really infinite in spatial extent or not.

All we know about this issue from observation is that it is (in the
region in which we can observe) consistent with being spatially flat
on the largest length scales.  If it really *is* flat and doesn't
have some type of flat-but-bounded topology such as a 3-torus, *then*
it really is infinite.  If the spatial sections of the spacetime of
the universe have some sort of flat-but-bounded topology, then, in
principle, we might be able to detect some of the necessary
anisotropy in the universe because all such finite-flat topologies
are *not* isotropic.  The only 3-d topological shape that is both
isotropic and homogeneous, as well as really flat is the infinite
space R^3.

Inflationary cosmological/high energy theory really doesn't answer
the question as to whether or not the universe is actually spatially
infinite or not.  What it *does* predict is regardless of whether or
not its initial spatial curvature was positive (and hence spatially
finite), or zero or negative (and hence spatially infinite, assuming
it is also both homogeneous and isotropic) that the process of
inflation during the inflationary epoch *so* stretched it out *so*
much that currently any possible finite curvature scale size is many
orders of magnitude larger than the horizon length, and, thus, it is
impossible to detect any positive or negative deviation from spatial
flatness on the largest observable length scales.  So whether or not
the universe is spatially finite, its size is *at least* many orders
of magnitude larger than the horizon distance, and that size is
perfectly consistent with being actually infinite.

The fact that observations of the deceleration parameter q indicate
that it seems to be negative (i.e. the universe's expansion rate
seems to be accelerating) strongly suggests that the universe has a
nonzero repulsive value for the cosmological constant.  In order for
the current observations to be explained it is necessary that the
background effective energy density associated with the cosmological
constant be about twice as large as the actual average energy
density of all the radiation and the matter in the universe, *and*
that the sum of both of these energy densities is just enough to
make the universe spatially flat (within observational error).

David Bowman