From: Ka Chun Yu
Subject: Re: [ASTRO] Big Bang Bashing
Date: Mon, 22 Feb 1999
I just came back from a talk by David Spergel who spoke briefly
about some possible future observations that definitely fall into the "amazing
discoveries" camp. Spergel is a cosmologist who is part of the MAP mission
team, and has come up with co-authors some intriguing ideas about the topology
of the universe. No not just its geometry--the description of spacetime associated
with the universe—but its topology.
The most basic idea behind the topology of the universe is
whether the universe has positive, negative, or zero curvature, i.e., whether
it is closed, open, or flat. Now let's assume that the universe is open, or
hyperbolic, as some observations are beginning to suggest. Then there are
two different sub-categories of open universes: infinite and compact, meaning
the universe could go on forever in any direction that you looked, or it could
double back on itself. The former category could be an open saddle; the latter
could be exemplified by a torus (or a doughnut). The topology of a doughnut
is neither flat nor closed in a positive sense, and is also different from
an infinite open saddle in the sense that if you traveled far enough in any
one direction along the surface of the doughnut, you'd arrive back at where
you had started.
Now it turns out that topologically, there are an infinite
number of different compact hyperbolic surfaces. Since compact hyperbolic
surfaces are similar to closed universes in that you can return to or look
back at the same point in space (or more technically, the topological manifold
is tiled in an infinite 4-D space by our 3-D universe), there are in principle
ways to check to see if our universe is in fact a compact hyperbolic. Given
the right topology, if we look far enough in any direction in space, we should
be able to see ourselves.
Here's where things get really tricky to envision... Another
way to think about this is to imagine the light bubble of our currently observable
universe to be bounded by a cube with mirrors at the face of each cube. (The
size of this cube would depend on the exact negative curvature of universe).
You would then have a hall of mirrors effect whereby if you were able to look
far enough in any one direction, you could see multiple copies of your universe.
You can't in principle look infinitely far because of the light travel time,
but if your observable horizon expands so that your horizon intersects these
mirrors, then the horizon of your universe would start to intersect with itself
on the opposite side.
Intersecting horizons of the universe will occur initially
as single points which then grow into circles. Now if the distance to the
next copy of our universe is less than the last scattering surface in the
cosmic microwave background, then one can in principle detect these circles
in the CMB. There are many topologies of a compact hyperbolic universe which
have effects at angular scales which could be detected by MAP or Planck (in
fact, there are infinitely many of these topologies). Thus if all of these
analyses hold up and if our universe is hyperbolic and compact, then in the
future, it is possible that not only will we know that the universe is open,
but we'll know its shape too.
Center for Astrophysics and Space Astronomy, University
of Colorado, Boulder, CO 80309
