Pavel said:
... good reasons to believe the Universe is infinite. They don't mention what those reasons are, but I was wondering if somebody could comment on that. Besides the anthropic principle, which I'm not even sure is popular among scientists, I'm not aware of any other compelling reasons.
...
I am not aware of any scientific reason to believe the Universe is spatially infinite.
It is an ASSUMPTION which is convenient mathematically and which is bound up in some people's minds with certain inflation scenarios that depend on exotic matter (the "inflaton field").
The actual data is consistent with the universe being NEARLY spatially flat but with a slight positive curvature (mathematically, an Omega of around 1.01) leading to a boundaryless spatially finite picture.
The data is also consistent with infinite space and curvature that is either zero or miniscule (corresponding to an Omega of say 1.00001, such as might result due to random variation in certain inflation stories.)
My advice would be to disregard what is said for public consumption (whether by Krauss or by Vilenkin) and look at recent technical papers by working observational cosmologists. Ned Wright would be a good one to start with: he came out with a paper in January 2007 that has a "best fit" value of Omega.
Whether someone says spatial finite or spatial infinite depends on things like prejudice, convenience, and what model they are using. Strictly on scientific grounds one cannot say it is one or the other.
Ned Wright is just an observational cosmologist, he doesn't favor one or the other. On page 17 of the paper he says
"Using all the data together gives the plot shown in Figure 6. The best fit model is
slightly closed with Omega_tot = 1.011..." If you want to check out the other options he discusses, here is the paper:
http://arxiv.org/abs/astro-ph/0701584
Constraints on Dark Energy from Supernovae, Gamma Ray Bursts, Acoustic Oscillations, Nucleosynthesis and Large Scale Structure and the Hubble constant
Edward L. Wright (UCLA)