In message .com,
Bruce writes
Seeing a picture of an Einstein Ring got me wondering. Do you suppose
that a light beam that departs something going one direction would
eventually pass a light beam that departs the same source in very
different direction?


So I'm a little perplexed with the question of how we might know that
this is what we're seeing, if it is. It would be a real shame if we
could theoretically see the same object many times but that the amount
of dark matter is so great that no light beam can actually make a round
trip.


You might look up the idea that the universe is a dodecahedron, which
will apparently have an effect on the spectrum of the CMB. Look at
http://physicsweb.org/article/news/7/10/5 for instance.
Another way this is being examined is to see if there are actual
repeating patterns in the background. Here's an example
http://www.etsu.edu/math/gardner/aas/empir.htm
I don't know if anyone's looked for repeating patterns in the 3D
structure of the universe. I'd think it would be impossible to tell,
given the billions of years that have passed since the light set out.
There are lots of other possibilities if the universe isn't a simple
"flat" structure. Try "horn universe", for instance
http://www.newscientist.com/article.ns?id=dn4879
Of course, going even further out there's the idea that the CMB might
have an artificial pattern, in which case there's possibly no way to
tell the real shape :-)