What shape is the Universe then?

Now that I have given you an idea of the different possible shapes
our Universe might have (and probably a headache along the way),
I will briefly review some of the recent discoveries and ideas in
cosmology and what they tell us about the Universe. After all, if
the Universe is going to one day collapse again in a Big Crunch I think the public have a right to know. It may not be for another
zillion years, but some people might just sleep more soundly if
they were told.
As I have already mentioned, whether the Universe is open,
closed or flat depends on how much matter it contains. This is,
however, a bit of a problem if the Universe is infinite in size,
because then it would also have to contain an infinite amount of
matter, however thinly it was spread out! The reason for this is the
cosmological principle which states that every part of the Universe
is pretty much like every other and so the density of matter is
roughly constant on the largest scale. This is a bit like saying that
even though only one in every thousand rooms in Hotel Infinity
is occupied, there would still be an infinite number of guests. So
instead, physicists talk about the density of matter. This is the
amount of matter per unit volume of space which should be a
sensible number even if the overall volume is infinite.
If the Universe has a matter density that is more than a certain
critical amount then the gravity of all this matter combined will be
able to halt the expansion and cause it to recollapse. On the other
hand, if the density is less than this critical amount then gravity can
only slow down the expansion to a constant rate and never stop it.
The Universe would be doomed to eternal expansion. Strangely
enough, many cosmologists have good reason to believe that the
density should be poised exactly at the critical value: balanced on
a knife’s edge between a universe that will one day collapse and
one that will steadily expand forever. Instead, the density of matter
would be such that its gravity will steadily slow the expansion rate
down until it finally stops expanding. However, it would literally
take forever for this to happen, so there would be no collapse.
This corresponds to a flat universe, neither open nor closed. How
did cosmologists come to believe that such an unlikely scenario is
possible and why should they want it to be so?
The fact is that, as far as our telescopes can see, the Universe
looks absolutely flat. It does not appear to have either positive
or negative curvature. This was quite a problem for cosmologists
since it was hard to believe that there would be precisely the right
density of matter to keep space flat. If this were the case then gravity would always be applying the brakes on the expansion,
continually slowing it down. This differs froma negatively curved
open universe (with a density less than the critical amount) because
in that case gravity would slow the expansion down only to some
steady constant rate at which it would settle into forever.
Most cosmologists believe that the flatness problem has now
been solved due to something called inflation. The simple
explanation for the flatness of space that we observe would be if
the Universe were much bigger thanwethink. In the same way,we
do not observe the curvature of the Earth because we can only see a
small part of the surface. The problem with this explanation is that
the Universe does not appear to be old enough to have expanded
to such a size. It is therefore thought that, when the Universe was
just a fraction of a second old, it underwent a very short period
of rapid expansion in which it grew to a size that was a trillion
trillion trillion trillion times the size it was before. This number is
unbelievably large and would be written as a one with 48 zeros!
Thus, the Universe could have been curled up before the period
of inflation. Then, in much less than a blink of an eye, it grew to
such a size that we would never be able to detect any curvature,
however far out in space we looked. This inflationary model of
the Universe therefore requires the density to be very close to the
critical value that would make it flat. In the mathematics, this
density is denoted by the capital Greek letter omega (written as ).
If the density is at the critical value, corresponding to flat space, we
say omega has a value of one. If the Universe is positively curved
and closed then omega is greater than one, and if it is negatively
curved and open then omega is less than one.
We are not sure whether or not this rapid inflation of the very
young Universe took place. Most cosmologists believe that it did,
but the arguments for and against it are subtle and rely on anumber
of different issues, some of which have not been resolved yet.
Is it possible to measure the density of matter in the Universe
directly? Cosmologists are confident it is. They rely on the
cosmological principle which, if you remember, states that the
Universe looks the same everywhere. In other words the density
of matter everywhere is the same as it is in our little corner of the Universe. Of course by ‘little corner’ I mean the part of the
Universe that we can see. So what do they see? It turns out that
the density of matter visible to us (that is the number of galaxies in
a given volume of space) is about one per cent of the critical value
required for a flat universe. Oh, oh, we have a problem! Where
could the other ninety nine per cent be?