Dynamics of the non-diagonal Bianchi IX model near the cosmological singularity

Details Dynamics of the non-diagonal Bianchi IX model near the cosmological singularity Dynamics of the non-diagonal Bianchi IX model near the cosmological singularity

2012-02-24

arxiv.org/abs/1202.5448v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

19 pages, no figures, revtex4; misleading misprint removed

Scientific paper

The mathematical structure of the six dimensional physical phase spaces of the non-diagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity. Critical points of the Hamiltonian equations appearing at infinities are of the nonhyperbolic type. Specific transformations of the phase space, including projection into finite region, do not change this type of criticality which is difficult for investigation by standard analytical tools. The nonhyperbolicity seems to be a generic feature of considered singular dynamics. The information that can be obtained from the linearized vector field is inconclusive. Making use of the physical Dirac observables as the phase space coordinates lowers substantially the dimensionality of the dynamics arena. Here, using commonly known methods for studying the dynamics may turn out to be quite satisfactory.

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