New Scale Factor Measure
  The computation of probabilities in an eternally inflating universe requires
a regulator or "measure". The scale factor time measure truncates the universe
when a congruence of timelike geodesics has expanded by a fixed volume factor.
This definition breaks down if the generating congruence is contracting---a
serious limitation that excludes from consideration gravitationally bound
regions such as our own. Here we propose a closely related regulator which is
well-defined in the entire spacetime. The New Scale Factor Cutoff restricts to
events with scale factor below a given value. Since the scale factor vanishes
at caustics and crunches, this cutoff always includes an infinite number of
disconnected future regions. We show that this does not lead to divergences.
The resulting measure combines desirable features of the old scale factor
cutoff and of the light-cone time cutoff, while eliminating some of the
disadvantages of each.
