Breaking radio silence here to report on some of the actual work I've been able to complete: a new paper with Heywood Tam.
Unitary Evolution and Cosmological Fine-Tuning Authors: Sean M. Carroll, Heywood Tam (Submitted on 8 Jul 2010) Abstract: Inflationary cosmology attempts to provide a natural explanation for the flatness and homogeneity of the observable universe. In the context of reversible (unitary) evolution, this goal is difficult to satisfy, as Liouville's theorem implies that no dynamical process can evolve a large number of initial states into a small number of final states. We use the invariant measure on solutions to Einstein's equation to quantify the problems of cosmological fine-tuning. The most natural interpretation of the measure is the flatness problem does not exist; almost all Robertson-Walker cosmologies are spatially flat. The homogeneity of the early universe, however, does represent a substantial fine-tuning; the horizon problem is real. When perturbations ...
