Robin Collins, professor of philosophy at Messiah College, who also holds a PhD. in physics, has written much about the fine-tuning argument, as well as other topics pertinent to science, religion, and ID. Recently I emailed him, asking about Bradley Monton's argument that based on the WMAP evidence, we should view the universe as infinite. He has allowed me to reprint his reply:
The WMAP evidence certainly is consistent with an infinite universe, but I would not say it is probably infinite. Two reasons. First, WMAP only shows that is very close to being flat, which still allows for the possibility that it has a small finite curvature, in which case it is finite. Second, a spatially flat universe does not imply an infinite universe.
For a flat universe, there is zero spatial curvature everywhere. The simplest geometrical object to which this corresponds to is a 3-dimensional flat hypersurface that extends to infinity. In this case, the universe is spatially infinite, with a similar mass-energy density to our own everywhere (given the starting assumptions of large-scale homogeneity and isotropy). Not all universes with spatially flat geometries are infinite in extent, however. In fact, there are ten other possibilities in which the hypersurface is locally flat but nonetheless closes back in on itself, thus forming a finite universe, the most familiar is the being the 3-Torus. One way of understanding how a finite universe is compatible with its being locally flat everywhere is to note that spatial curvature is a local notion defined by the intrinsic property of the space at every point. The overall topological structure – which determines whether the universe is finite or infinite – is a global notion that is constrained though usually not completely determined by the local curvature. [Footnote: When embed a two-dimensional closed surface—such as a torus-- in a three dimensional space, it looks curved, leading us to think that if a space is topologically closed, it must be curved. This reasoning is faulty: the embedding space can induce a curvature that is not the same as the intrinsic curvature as it is defined mathematically using the metric. (See Carroll, pp. ____).]
So perhaps we live in an infinite universe, but there are other ways of interpreting the evidence.