Quantum theory of the Bianchi II model

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.

arXiv comment12 pages, 3 figures, version accepted by PRD

References in corpus (7)

• Loop quantum cosmology of Bianchi I models
• Loop quantum cosmology of Bianchi type IX models
• Loop quantum cosmology of Bianchi type II models
• Wavefunctions for Highly Anisotropic Homogeneous Cosmologies
• Reduced phase space approach to Kasner universe and the problem of time in quantum theory
• Bianchi I model in terms of nonstandard loop quantum cosmology: Classical dynamics
• Bianchi I model in terms of nonstandard loop quantum cosmology: Quantum dynamics

Cited by in corpus (3)

• Singularity avoidance in a quantum model of the Mixmaster universe
• Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe
• Semiclassical study of the Mixmaster model: the quantum Kasner map