Global phase time and wave function for the Kantowski-Sachs anisotropic universe

TL;DR

This paper presents a consistent quantum cosmological model for the Kantowski-Sachs universe, defining a clear notion of time and evolution through a specific coordinate choice, and solving the Wheeler-DeWitt equation for definite energy states.

Contribution

It introduces a novel approach to quantize the Kantowski-Sachs model with a well-defined time, linking solutions to two equivalent theories on different constraint surface sheets.

Findings

Solution of Wheeler-DeWitt equation in definite energy states

Clear notion of time and evolution in anisotropic quantum cosmology

Two disjoint but equivalent theoretical frameworks

Abstract

A consisten quantization with a clear notion of time and evolution is given for the anisotropic Kantowski-SDachs cosmological model. It is shown that a suitable coordinate choice allows to obtain a solution of the Wheeler-DeWitt equation in the form of definite energy states, and that the results can be associated to two disjoint equivalent theories, one for each sheet of the constraint surface.