Decoherent histories approach to the cosmological measure problem

Abstract

The method of decoherent histories allows probabilities to be assigned to sequences of quantum events in systems, such as the universe as a whole, where there is no external observer to make measurements. This paper applies the method of decoherent histories to address cosmological questions. Using a series of simple examples, beginning with the harmonic oscillator, we show that systems in a stationary state such as an energy eigenstate or thermal state can exhibit decoherent histories with non-trivial dynamics. We then examine decoherent histories in a universe that undergoes eternal inflation. Decoherent histories that assign probabilities to sequences of events in the vicinity of a timelike geodesic supply a natural cosmological measure. Under reasonable conditions, such sequences of events do not suffer from the presence of unlikely statistical fluctuations that mimic reality.