Measures on Transitions for Cosmology from Eternal Inflation

We argue that, in the context of eternal inflation in the landscape, making predictions for cosmological—and possibly particle physics—observables requires a measure on the possible cosmological histories as opposed to one on the vacua themselves. If significant slow-roll inflation occurs, the observables are generally determined by the history after the last transition between metastable vacua. Hence, we start from several existing measures for counting vacua and develop measures for counting the transitions between vacua.

Figure 1

A simple potential landscape. We consider both a positive and negative energy $C$ well, with the zeros in energy density denoted by the solid or the dotted line. In the text, we discuss both three-well [composed of $(A,B,C)$] and four-well [composed of $(A,B,C,D)$] landscapes.