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/H 4 = 3/(2π 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.
- Cosmology of theories beyond the SM
- Space-time symmetries
- Spacetime singularities
ASJC Scopus subject areas
- Nuclear and High Energy Physics