Wallace said:
Another useful term to look for is 'scale of homogeneity', I think that might get you quickly to the heart of the matter.
Well, gentlemen, (and MeJennifer) after carefully examining these articles on the scale of homogeneity, I don't think they are as conclusive as a few of you might imagine. I looked at some of these papers and they fall into two general categories to extend the homogeneity beyond the range of the visible universe. One category uses the recession data and another uses the CMB data.
One typical article in support of the cosmological principle is Martinez’s "Searching for the Scale of Homogeneity:"
http://www.ingentaconnect.com/content/bsc/mnr/1998/00000298/00000004/art00024
Using the red shift recession data, it claims "no hope for unbounded fractal distributions," which basically supports a total projection of the visible homogeneity. However, he bases his presumption on the
two point correlation function which is dependent on the
fair sample hypothesis which is itself a derivative of the cosmological principle. This is like saying, if the universe were homogeneous then it could be modeled like this and since the model is so beautifully compliant with respect to relativity then it is undoubtedly true.
This approach constitutes the same potentially true but ultimately false presumptions we have always made when characterizing the universe beyond the data at hand. We always make the presumption that the data we have is sufficient to explain "everything." This is what the cosmological principle is doing for us in modern cosmology. It makes an infinite universe compliant to a finite data set. But historically, the universe has always proven to be more diverse than is possible to determine from any finite local data set.
You may be surprised to find that there are also articles that do not explicitly support a totally homogeneous universe. Take Patricia Castro’s "Scale of Homogeneity from WMAP" which states:
http://arxiv.org/abs/astro-ph/0309320
"We review the physics of the Grishchuck-Zel'dovich effect which describes the impact of large amplitude, super-horizon gravitational field fluctuations on the Cosmic Microwave Background anisotropy power spectrum. Using the latest determination of the spectrum by WMAP, we infer a lower limit on the present length-scale of such fluctuations of 3927 times the cosmological particle horizon (at the 95% confidence level)."
Attacking the problem from a lower limit perspective is a far better strategy than presuming homogeneity and trying to indicate the absence of an upper limit. This approach addresses only what we can be confident in with respect to the local data rather than trying to corroborate an impossible thesis with a potential to range infinitely beyond the local data set.
If we were living on an electron of a hydrogen atom in the middle of the ocean, we would be perfectly justified in presuming the universe was made entirely of water molecules, and all our calculations would work perfectly, but we would still be wrong. All I'm saying is that a Bayesian examination across the widest possible spectrum of the existing data (the hierarchical structure of of the known material universe from quarks to galaxy clusters and across the history of scientific investigation) says that the universe is hierarchical and not homogeneous across all scales and that whenever we try to terminate that hierarchy is precisely where our theories have historically proven weakest. And the CP is that point of weakest presumption in modern cosmology.
For people to get upset to the point of indignation over the suggestion that the Big Bang may ultimately be a finite phenomenon is more an artifact of psychology than of science. The universe is not ours to claim total understanding beyond a reasonable projection of the data to a statistically relevant degree. That it is possible for the cosmological principle to be true is not the same thing as being inevitable.
-Mike