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Nonadiabatic bounce and an inflationary phase in the quantum mixmaster universe

Hervé Bergeron*

Ewa Czuchry†

Jean-Pierre Gazeau‡

Przemysław Małkiewicz§

  • ISMO, CNRS, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France

  • National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa, Poland

  • APC, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Obs de Paris, Sorbonne Paris Cité, France and Centro Brasileiro de Pesquisas Fisicas, 22290-180 Rio de Janeiro, RJ, Brazil

  • National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa, Poland and APC, Université Paris Diderot, CNRS/IN2P3, CEA/Irfu, Obs de Paris, Sorbonne Paris Cité, 75205 Paris, France

  • *herve.bergeron@u-psud.fr
  • †eczuchry@fuw.edu.pl
  • ‡gazeau@apc.univ-paris7.fr
  • §pmalk@fuw.edu.pl
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Phys. Rev. D 93, 124053 – Published 21 June, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.124053

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 that 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.

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Smooth quantum dynamics of the mixmaster universe

Hervé Bergeron, Ewa Czuchry, Jean-Pierre Gazeau, Przemysław Małkiewicz, and Włodzimierz Piechocki
Phys. Rev. D 92, 061302(R) (2015)

Article Text

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Phys. Rev. D 93, 124053– Published 21 June, 2016
  • Received 26 November 2015

© 2016 American Physical Society

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