  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. We show that there exists a critical
value for the classical inflaton speed, \dot\phi^2/H^4 = 3/(2 \pi^2), 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 show 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. Our analysis represents the
exact quantum treatment of the system at lowest order in the slow-roll
parameters and H^2/M_Pl^2.
