Generalized Quantum Theory of Recollapsing Homogeneous Cosmologies

TL;DR

This paper develops a generalized quantum theory framework for recollapsing homogeneous cosmological models, enabling calculation of decoherence and probabilities of classical and non-classical universe evolutions.

Contribution

It introduces a sum-over-histories quantum approach for Bianchi cosmologies, providing new methods to compute decoherence and classicality probabilities.

Findings

Probabilities for classical recollapse are near unity under certain conditions.

Decoherence of alternative histories is demonstrated for specific initial conditions.

Generalized the

Abstract

A sum-over-histories generalized quantum theory is developed for homogeneous minisuperspace type A Bianchi cosmological models, focussing on the particular example of the classically recollapsing Bianchi IX universe. The decoherence functional for such universes is exhibited. We show how the probabilities of decoherent sets of alternative, coarse-grained histories of these model universes can be calculated. We consider in particular the probabilities for classical evolution defined by a suitable coarse-graining. For a restricted class of initial conditions and coarse grainings we exhibit the approximate decoherence of alternative histories in which the universe behaves classically and those in which it does not. For these situations we show that the probability is near unity for the universe to recontract classically if it expands classically. We also determine the relative probabilities of quasi-classical trajectories for initial states of WKB form, recovering for such states a precise form of the familiar heuristic "J d\Sigma" rule of quantum cosmology, as well as a generalization of this rule to generic initial states.