Bianchi IX model: Reducing phase space

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.

21 pages, no figures, published in Phys. Rev. D

References in corpus (12)

• Loop Quantum Cosmology: A Status Report
• Classical and Quantum Features of the Mixmaster Singularity
• A Hamiltonian Formulation of the BKL Conjecture
• Turning Big Bang into Big Bounce: I. Classical Dynamics
• Mixmaster: Fact and Belief
• A new proof of the Bianchi type IX attractor theorem
• Reduced phase space approach to Kasner universe and the problem of time in quantum theory
• A Dynamical Systems Approach to Schwarzschild Null Geodesics
• Bianchi I model in terms of nonstandard loop quantum cosmology: Quantum dynamics
• Evolution in bouncing quantum cosmology
• Gaussian state for the bouncing quantum cosmology
• Bounce scenarios in the Sotiriou-Visser-Weinfurtner generalization of the projectable Horava-Lifshitz gravity

Cited by in corpus (11)

• Dynamical analysis of anisotropic scalar-field cosmologies for a wide range of potentials
• Qualitative analysis of Kantowski-Sachs metric in a generic class of $f(R)$ models
• Quantum Belinski-Khalatnikov-Lifshitz scenario
• Timelike BKL singularities and chaos in AdS/CFT
• Robustness of the quantum BKL scenario
• Origin of Structure in the Universe: Quantum Cosmology Reconsidered
• Quantum dynamics corresponding to chaotic BKL scenario
• Generic instability of the dynamics underlying the Belinski-Khalatnikov-Lifshitz scenario
• The dynamics of general Bianchi IX model near the cosmological singularity
• Comparing the dynamics of diagonal and general Bianchi IX spacetime
• Dynamical structures specific to strong gravitational field: Quantum formalism