Decoherent histories approach to the cosmological measure problem

TL;DR

This paper applies the decoherent histories framework to cosmology, demonstrating how it can assign probabilities to universe-wide events and address the measure problem in eternal inflation scenarios.

Contribution

It introduces a novel application of decoherent histories to cosmology, providing a method to define probabilities without external observers in universe models.

Findings

Decoherent histories can describe non-trivial dynamics in stationary quantum states.

The approach offers a natural cosmological measure near geodesics in eternal inflation.

It avoids unlikely fluctuations that mimic reality in probability assignments.

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.