The Phase Transition to Eternal Inflation
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/MPl2.
We analytically examine output persistence from monetary shocks in a DSGE model with staggered prices or wages under a Taylor Rule. Surprisingly, while Taylor-style staggering never yields persistence, Calvo-style staggering of wages does generate persistence under decreasing returns to labour.