Unitary evolution for anisotropic quantum cosmologies: models with variable spatial curvature

TL;DR

This paper demonstrates that certain anisotropic quantum cosmological models with variable spatial curvature, specifically Bianchi type VI and II, can exhibit unitary evolution through explicit solutions or self-adjoint extensions of the Wheeler-DeWitt equation.

Contribution

It provides new examples of unitary quantum cosmological models with variable spatial curvature, expanding the understanding of quantum evolution in anisotropic universes.

Findings

Explicit unitary solutions for Bianchi type VI and II models.

Existence of self-adjoint extensions for the Wheeler-DeWitt operator.

Challenging the belief that anisotropic models cannot have unitary evolution.

Abstract

Contrary to the general belief, there has recently been quite a few examples of unitary evolution of quantum cosmological models. The present work gives more examples, namely Bianchi type VI and type II. These examples are important as they involve varying spatial curvature unlike the most talked about homogeneous but anisotropic cosmological models like Bianchi I, V and IX. We exhibit either explicit example of the unitary solutions of the Wheeler-DeWitt equation, or at least show that a self-adjoint extension is possible.