Quantum theory of the Bianchi II model

TL;DR

This paper develops a quantum description of the vacuum Bianchi II universe, analyzing the transition amplitudes between quantum states and highlighting differences from classical predictions at small momentum values.

Contribution

It provides a quantum framework for Bianchi II cosmology and connects it to the quantum evolution of the Bianchi IX universe, emphasizing the role of uncertainty at small scales.

Findings

Classical and quantum results agree at large momentum values.

Quantum effects become significant at small momentum values due to the Heisenberg uncertainty principle.

The approach offers insights into the quantum behavior of anisotropic cosmological models.

Abstract

We describe the quantum evolution of the vacuum Bianchi II universe in terms of the transition amplitude between two asymptotic quantum Kasner-like states. For large values of the momentum variable the classical and quantum calculations give similar results. The difference occurs for small values of this variable due to the Heisenberg uncertainty principle. Our results can be used, to some extent, as a building block of the quantum evolution of the vacuum Bianchi IX universe.