Nonadiabatic bounce and an inflationary phase in the quantum mixmaster universe

TL;DR

This paper analyzes the quantum dynamics of the Bianchi IX universe, revealing a phase transition that leads to anisotropy production and an inflationary phase during the bounce, using a harmonic approximation and analytical methods.

Contribution

It introduces a new analysis of quantum anisotropic oscillations in the mixmaster universe, identifying a phase transition that triggers inflationary behavior.

Findings

Identification of a critical parameter for phase transition

Detection of large anisotropy production at the bounce

Prediction of a sustained inflationary phase

Abstract

Following our previous paper, Bergeron et al, Smooth quantum dynamics of the mixmaster universe, Phys. Rev. D 92, 061302(R) (2015), concerning the quantization of the vacuum Bianchi IX model and the Born-Huang-Oppenheimer framework, we present a further analysis of the dynamical properties of the model. Consistently with the deep quantum regime, we implement the harmonic approximation of the anisotropy potential. We thus obtain manageable dynamical equations. We study the quantum anisotropic oscillations during the bouncing phase of the universe. Neglecting the backreaction from transitions between quantum anisotropy states we obtain analytical results. In particular, we identify a parameter which is associated with dynamical properties of the quantum model and describes a sort of phase transition. Once the parameter exceeds its critical value, the Born-Huang-Oppenheimer approximation breaks down. The application of the present result to a simple model of the Universe indicates that the parameter indeed exceeds its critical value and that there takes place a huge production of anisotropy at the bounce. This in turn must lead to a sustained phase of accelerated expansion, an inflationary phase. The quantitative inclusion of backreaction shall be examined in a follow-up paper based on the vibronic approach.