Inhomogeneous Quantum Mixmaster: from Classical toward Quantum Mechanics

TL;DR

This paper explores the quantum features of the inhomogeneous Mixmaster universe by analyzing its Hamiltonian formulation, operator ordering, and quantum dynamics, revealing a discrete spectrum and a non-zero ground state energy related to anisotropies.

Contribution

It provides a detailed quantum description of the inhomogeneous Mixmaster model, including operator ordering, spectrum analysis, and ground state characterization, bridging classical and quantum cosmology.

Findings

Discrete spectrum with analytic expressions at high occupation numbers

Ground state characterized by non-zero zero-point energy

Quantum dynamics consistent with classical Liouville theorem

Abstract

Starting from the Hamiltonian formulation for the inhomogeneous Mixmaster dynam- ics, we approach its quantum features through the link of the quasi-classical limit. We fix the proper operator-ordering which ensures that the WKB continuity equation overlaps the Liouville theorem as restricted to the configuration space. We describe the full quantum dynamics of the model in some details, providing a characterization of the (discrete) spectrum with analytic expressions for the limit of high occupation number. One of the main achievements of our analysis relies on the description of the ground state morphology, showing how it is characterized by a non-vanishing zero-point energy associated to the Universe anisotropy degrees of freedom