In my paper “Design Inferences in an Infinite Universe”, I explore the status of design inferences under the assumption that the universe is spatially infinite. From a philosopher’s standpoint, this project has interest regardless of whether the universe is actually spatially infinite. But I do hold that whether the universe is spatially infinite can affect the strength of some design arguments for the existence of God, and hence, if one wants to know whether God actually exists in this universe, it could be relevant to establish whether the universe is spatially infinite. 

I didn’t try to establish that in my paper — to look at the evidence for and against the hypothesis that the universe is spatially infinite would take at least a whole paper, and would quickly get into some sophisticated physics. But I did provide two paragraphs of support for the hypothesis that the universe is spatially infinite, just to show that it is a live possibility amongst physicists. I got the following email in reply:

I have read your preprint with great interest. But,
allow me to say, you assume an infinite universe,
which is far from proven or accepted:

“The next question about the shape of the Universe is
to know whether space is finite or infinite –
equivalent to know whether space contains a finite or
an infinite amount of matter–energy, since the usual
assumption of homogeneity implies a uniform
distribution of matter and energy through space. From
a purely geometrical point of view, all positively
curved spaces are finite whatever their topology, but
the converse is not true : flat or negatively
curved spaces can have finite or infinite volumes,
depending on their degree of connectedness (Ellis,
1971 ; Lachièze-Rey & Luminet, 1995).”


“The new release of WMAP data (Spergel et al., 2006),
integrating two additional years of observation with
reduced uncertainty, strengthened the evidence for an
abnormally low quadrupole and other features which do
not match with the infinite flat space model (this
explains the unexpected delay in the delivery of this
second release, originally announced for February


I would be happy to see those alternatives integrated
in your excellent paper.

I mostly agree with this email (especially the part about my paper being excellent) — a flat space (i.e. a space with no global curvature) can have a finite volume, as a result of having a certain topology, and there is some evidence for connected topologies in the WMAP data. As far as I can tell, though, most physicists who pay attention to this sort of thing still think that the WMAP data is providing evidence for the hypothesis that the universe is spatially infinite. See, for example, this:

If the density just equals the critical density, the universe is flat, but still presumably infinite. The value of the critical density is very small: it corresponds to roughly 6 hydrogen atoms per cubic meter, an astonishingly good vacuum by terrestrial standards! One of the key scientific questions in cosmology today is: what is the average density of matter in our universe? While the answer is not yet known for certain, it appears to be tantalizingly close to the critical density.

Anyway, going back to the email, I’m surprised by the claim that the second release of WMAP data was unexpectedly delayed because it’s providing evidence for features that don’t match the infinite flat space model. This sounds like a strange sociological/conspiracy-theory type claim (I’m not sure exactly how to categorize it). I haven’t found anything definitive online, but I did find this:

Conspiracy theories abound on the delay in releasing WMAP year 2 results. The WMAP people are simply not talking, so take anything you see on the web with a healthy dose of salt. 

The fact that the author of that paper the email quotes from was willing to definitely state the reason that the data was delayed, with no support to back up that claim, makes me somewhat worried about the intellectual quality and the objectivity of the rest of the paper. 

Anyway the data are out now. They don’t seem to have anything especially definitively new to say about whether the universe is spatially infinite.