Quantum Cosmology of Kantowski-Sachs like Models

TL;DR

This paper solves the Wheeler-DeWitt equation for a class of Kantowski-Sachs like models, including joined and generalized models, analyzing wave functions, boundary conditions, and implications for the arrow of time.

Contribution

It provides an exact solution to the Wheeler-DeWitt equation for complex Kantowski-Sachs models, including joined configurations and boundary condition analysis.

Findings

Exact solutions for Wheeler-DeWitt equation in Kantowski-Sachs models

Product structure of wave functions in joined models with correlations

Impact of boundary conditions on the arrow of time

Abstract

The Wheeler-DeWitt equation for a class of Kantowski-Sachs like models is completely solved. The generalized models include the Kantowski-Sachs model with cosmological constant and pressureless dust. Likewise contained is a joined model which consists of a Kantowski-Sachs cylinder inserted between two FRW half--spheres. The (second order) WKB approximation is exact for the wave functions of the complete set and this facilitates the product structure of the wave function for the joined model. In spite of the product structure the wave function can not be interpreted as admitting no correlations between the different regions. This problem is due to the joining procedure and may therefore be present for all joined models. Finally, the {s}ymmetric {i}nitial {c}ondition (SIC) for the wave function is analyzed and compared with the ``no bouindary'' condition. The consequences of the different boundary conditions for the arrow of time are briefly mentioned.