Milne universe, chi-squared

Rocky Kolb (Fermilab) gave a talk about the possibility that small-scale (tens of Mpc) order-unity density perturbations can mysteriously produce cosmic acceleration. When various of us (Dvali, Gruzinov, me) asked him how, physically, small-scale variations that average to zero could affect large scales, he pointed to terms that don't obviously sum to small totals in a series expansion of cosmic perturbation theory in GR. In my view, the fact that Kolb can't sum a divergent infinite series is not an argument that acceleration is caused by small-scale inhomogeneities! But in particular, and to be concrete, since the universe he considers is non-relativistic matter (dust in GR parlance), I asked Kolb for a physical reason that the Milne calculations (ie, the derivation of the FRW Universe in an entirely Newtonian gravity framework) are wrong, as he must assert that they are (since they agree with the conventional GR calculations and show no acceleration). He said simply that it was possible that they are.

Masjedi, Berlind, Blanton, and I discussed hypothesis testing (in the context of Masjedi's project to fit halo occupation models to his small-scale correlation function. For the Nth time, I figured out the answer to a question first asked of me by Scott Tremaine (Princeton): If you have two equally plausible models to explain a set of data, a chi-squared difference of just one or two (in total chi-squared, not per degree-of-freedom) is sufficient to prefer one model over the other. But if you have a model, and you want to show that the model is not allowed by the data, you have to show that the model has a chi-squared that is significantly larger than the number of degrees of freedom. Of course both of these statements are only rigorously justified when you have a linear problem and uniform priors on the parameters and exactly gaussian (and well-known) uncertainties.