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Re: measuring the universe



In the monograph "Homogeneous Relativistic Cosmologies" by M. P. Ryan
and L. C. Shepley (Princeton 1975) it is explained how various cosmologies
can be intrinsicly classified with respect their isometry group. One large
collection of cosmologies (FRW models included) is called spatially
homogeneous, i.e. those homogeneous in space but not in time.

For the class of spatially homogeneous models, due to the isometries, one
has invariant spacelike hypersurfaces that might be compact ("closed"
in cosmological terms, mathematically closed and bounded by the Heine-
Borel theorem) or not. A model that has a compact spacelike hypersurface
at one cosmological time as read by clocks following the cosmological
fluid might later find its hypersurfaces to be noncompact. One example is
the T-NUT-M universe that evolves "from open to closed to open again".

Further there is another point that should be noted: The field equations
for GR are local. There is no input on global questions like topology.
One might close for example the hypersurfaces by demanding periodic boundary
conditions. Hopefully we will know more about the question about
topology when PLANCK has done its work. Until then I guess the question on
open or closed is still open.... :-)

----- Original Message -----
From: "John Denker" <jsd@MONMOUTH.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Saturday, August 12, 2000 10:12 PM
Subject: Re: measuring the universe


: At 12:48 PM 8/12/00 -0600, Jim Green wrote:
: >I thought "open" and "closed" were used to describe whether the Universe
: >would collapse or not -- ie whether the Universe would expand forever or at
: >some point start to contract to an eventual Big Crunch.
:
: Close, but not quite. Here's the deal:
:
: 1) A finite-sized universe (i.e. the kind that astronomers call "closed")
: is guaranteed to have a finite time-span as well, according to a wide range
: of cosmological models.
:
: You can cook up exceptions, e.g. by fiddling with the "cosmological
: constant" which can be used to introduce a bias into Einstein's equations.
:
: 2) An infinite-sized universe (i.e. the kind that astronomers call "open")
: may go crunch after a finite time, or may continue expanding forever. It
: depends on the initial conditions (or, if you like, present conditions) of
: mass density and expansion rate.
:
: >But this aside for a moment --and whether we can actually "see" (by
: >whatever means) to the "edge" of the Universe -- doesn't the current
: >standard model assume that the Universe is finite in size