Quantum Cosmology for the General Bianchi Type II, VI(Class A) and VII(Class A) vacuum geometries

TL;DR

This paper performs a canonical quantization of the most general vacuum Bianchi type II, VI, and VII cosmologies, reducing the minisuperspace models to their physical degrees of freedom using classical and quantum integrals of motion.

Contribution

It introduces a comprehensive quantization approach for the full minisuperspace models of these Bianchi types, including all scale factors, lapse, and shift variables.

Findings

Successful reduction to physical degrees of freedom.

Implementation of quantum integrals of motion.

Framework for quantum analysis of complex vacuum geometries.

Abstract

The canonical quantization of the most general minisuperspace actions --i.e. with all six scale factor as well as the lapse function and the shift vector present-- describing the vacuum type II, VI and VII geometries, is considered. The reduction to the corresponding physical degrees of freedom is achieved through the usage of the linear constraints as well as the quantum version of the entire set of classical integrals of motion.