Bianchi IX model: Reducing phase space

Ewa Czuchry and Włodzimierz Piechocki
Phys. Rev. D 87, 084021 – Published 8 April 2013

Abstract

The mathematical structure of higher-dimensional physical phase spaces of the nondiagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity by using dynamical system methods. Critical points of the Hamiltonian equations appear at infinities and are of a nonhyperbolic type, which is a generic feature of the considered singular dynamics. The reduction of the kinematical symplectic 2-form to the constraint surface enables the determination of the physical Hamiltonian. This procedure lowers the dimensionality of the dynamics arena. The presented analysis of the phase space is based on canonical transformations. We test our method for the specific subspace of the physical phase space. The obtained results encourage further examination of the dynamics within our approach.

  • Received 11 February 2013

DOI:https://doi.org/10.1103/PhysRevD.87.084021

© 2013 American Physical Society

Authors & Affiliations

Ewa Czuchry and Włodzimierz Piechocki

  • Department of Fundamental Research, National Centre for Nuclear Research, Hoża 69, PL-00-681 Warsaw, Poland

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Issue

Vol. 87, Iss. 8 — 15 April 2013

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