Re: Size of Universe

["John S. Denker" <jsd@MONMOUTH.COM>]

At 08:06 AM 10/10/01 -0700, Wes Davis wrote:

>     I recently attended a lecture on GR.
> I learned of  recent data indicating that
> the universe is flat.  How does this affect
> the size of the universe?  Is the universe
> finite, infinite, or is this not a sensible question?

There are several different questions in there.

First of all:  Note that "flat" refers to intrinsic curvature.  This is the
only sort of curvature that makes sense when talking about the universe...
but when visualizing models of the universe, you have to be careful not to
be confused by any extrinsic curvature.  In particular, take a flat piece
of paper.  It really is flat, i.e. zero intrinsic curvature.  Curl it up
into a cylinder.  It still has zero intrinsic curvature.  Flatlanders
living on the cylinder can't measure anything non-flat about it, unless
they manage to circumnavigate it.

1) A flat universe could well be infinite.

2) A flat universe could be like a cylinder, or a torus, that has zero
intrinsic curvature everywhere but nevertheless closes back on itself.  We
would AFAICT be unable to distinguish this from case (1), unless we managed
to circumnavigate the universe.

================

3) A lot of the time when people talk about infinite or non-infinite
universes, they are talking about the !time! duration not the spatial size.

Consider a universe with enough mass to give itself a positive curvature
(like a sphere) as opposed to having zero or negative curvature (like a
sombrero).  According to standard theories, such a universe will have
enough gravity to arrest and reverse the Hubble expansion, leading to a Big
Crunch at some finite time in the future.

So, if you buy the theory, a flat universe is special because it is just
barely Crunch-free.

OTOH competing theories are a dime a dozen.