Abstract. 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, ²/H⁴ = 3/(2π²), 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 H²/M_Pl².

Key words: Space-Time Symmetries; Cosmology of Theories beyond the SM; Spacetime Singularities

Received 16 May 2008, accepted for publication 12 August 2008
Published 5 September 2008