Measure Problem for Eternal and Non-Eternal Inflation

Abstract

We study various probability measures for eternal inflation by applying their regularization prescriptions to models where inflation is not eternal. For simplicity we work with a toy model describing inflation that can interpolate between eternal and non-eternal inflation by continuous variation of a parameter. We investigate whether the predictions of four different measures (proper time, scale factor cutoff, stationary and causal {diamond}) change continuously with the change of this parameter. We will show that {only} for the stationary measure the predictions change continuously. For the proper-time and the scale factor cutoff, the predictions are strongly discontinuous. For the causal diamond measure, the predictions are continuous only if the stage of the slow-roll inflation is sufficiently long.Comment: 9 pages, 4 figure