Volume Weighting the Measure of the Universe from Classical Slow-Roll
  Expansion
  One of the most frustrating issues in early universe cosmology centers on how
to reconcile the vast choice of universes in string theory and in its most
plausible high energy sibling, eternal inflation, that jointly generate the
string landscape with the fine-tuned and hence relatively small number of
universes that have undergone a large expansion and can accommodate observers
and, in particular, galaxies. We show that such observations are highly favored
for any system whereby physical parameters are distributed at a high energy
scale, due to the conservation of the Liouville measure and the gauge nature of
volume, asymptotically approaching a period of large isotropic expansion
characterised by $w=-1$. Our interpretation predicts that all observational
probes for deviations from $w=-1$ in the foreseeable future are doomed to
failure. The purpose of this paper is not to introduce a new measure for the
multiverse, but rather to show how what is perhaps the most natural and well
known measure, volume weighting, arises as a consequence of the conservation of
the Liouville measure on phase space during the classical slow-roll expansion.
