The Phase Transition to Eternal Inflation

TL;DR

This paper analyzes the phase transition to eternal inflation by examining the probability distribution of the reheating volume, identifying a critical inflaton speed where the distribution becomes infinite and eternal inflation begins.

Contribution

It provides an exact quantum analysis of the transition to eternal inflation, identifying a critical inflaton speed and characterizing the probability distribution of reheating volume.

Findings

Existence of a critical inflaton speed for phase transition

Infinite moments of the distribution below critical speed

Finite probability of infinite reheating volume at transition

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, \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.