Leonardo Senatore, Harvard University
The Phase Transition of Slow-Roll Eternal Inflation
December 5, 2007

For slow-roll inflation we study the phase-transition to the eternal regime.
Starting from a finite inflationary volume, we consider the volume of the
universe at reheating as order parameter. By performing an analysis that is the
exact quantum treatment at lowest order in slow-roll and H^2/M_Pl^2, we show
that there exists a critical value for the classical inflaton speed where the
probability distribution for the reheating volume undergoes a sharp transition.
In particular, for sub-critical inflaton speeds all distribution moments become
infinite. We argue that at the same transition point the system develops a
non-vanishing probability of having a strictly infinite reheating volume, while
retaining a finite probability for finite values.