Iggy Sawicki (Chicago) gave a very lively talk today about quantitative empirical tests of the leading cosmology-inspired modification of gravity: DGP (named after Dvali, Gabadadze, and Porrati, all here in the CCPP at NYU). The talk was lively because it is basically impossible to do exact calculations of the evolution of fluctuations (it is even hard to do the scale factor!) in this model; the arguments are all about the applicability of various possible approximations. In general, GR calculations are hard; modifications to GR are harder. We have a dangerous possible future in which no substantial competitors to GR ever get worked out. We might end up settling on GR just because it is the only exactly computed model!
After the talk, Blanton and I had a long discussion of the statistics involved in
ruling out models. A trivial point, but one that is often misunderstood, is that it is very different to ask the question
Is this model consistent with the data? than it is to ask the question
Is model A a significantly better fit to the data than model B? Sawicki showed that DGP is a significantly less good fit to the data than GR (ie, Lambda-CDM), but he did not show that either model is consistent with the data. I actually don't think that either is consistent with the data, in the technical sense (chi-squared on the order of the number of degrees of freedom). But of course this just reminds me that we don't make important decisions about the fundamental physics of the Universe on the basis of calculations in gaussian statistics!