Mixmaster dynamics in the dust time gauge

TL;DR

This paper explores the Hamiltonian dynamics of dust-filled Bianchi IX cosmology in dust time gauge, revealing oscillations between dust-Kasner solutions and deriving a generalized transition law, with implications for quantum cosmology.

Contribution

It introduces a novel physical picture of dust-Bianchi IX dynamics using a time-independent Hamiltonian and derives a generalized transition law including matter effects.

Findings

Oscillations between dust-Kasner solutions instead of vacuum-Kasner.

Derived a generalized transition law with matter component.

Performed path integral quantization and obtained an effective action.

Abstract

We study the Hamiltonian dynamics of the dust-Bianchi IX universe in dust time gauge. This model has three physical metric degrees of freedom, with evolution determined by a time-independent physical Hamiltonian. This approach gives a new physical picture where dust-Bianchi IX dynamics is described by oscillations between dust-Kasner solutions, rather than between vacuum-Kasner solutions. We derive a generalized transition law between these phases, which has a matter component. Sufficiently close to a singularity, we show that this law reduces to the vacuum Belinski-Khalatnikov-Lifshitz map. We include an analysis with dust and a scalar field. Lastly, we describe a path integral quantization using the dust-time physical Hamiltonian and derive an effective action for the dust-Kasner model by integrating out the anisotropy degrees of freedom.