The Mixmaster Universe in a generalized uncertainty principle framework
arXiv:0808.0831 · doi:10.1016/j.physletb.2009.10.003
Abstract
The Bianchi IX cosmological model is analyzed in a generalized uncertainty principle framework. The Arnowitt-Deser-Misner reduction of the dynamics is performed and a time-coordinate, namely the volume of the Universe, naturally arises. Such a variable is treated in the ordinary way while the anisotropies (the physical degrees of freedom) are described by a deformed Heisenberg algebra. The analysis of the model (passing through Bianchi I and II) is performed at classical level by studying the modifications induced on the symplectic geometry by the deformed algebra. We show that, the Universe can not isotropize because of the deformed Kasner dynamics, the triangular allowed domain is asymptotically stationary with respect to the particle (Universe) and its bounces against the walls are not interrupted by the deformed effects. Furthermore, no reflection law can be in general obtained since the Bianchi II model is no longer analytically integrable. This way, the deformed Mixmaster Universe can be still considered a chaotic system.
7 pages, minor changes
References in corpus (32)
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- Quantum gravity and minimum length
- A Generalized Uncertainty Principle in Quantum Gravity
- Quantum Nature of the Big Bang
- Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
- Quantum Groups, Gravity, and the Generalized Uncertainty Principle
- Loop Quantum Cosmology
- Nonpointlike Particles in Harmonic Oscillators
- Minimal Length Uncertainty Relation and Ultraviolet Regularisation
- Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
- Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
- Chaos in Superstring Cosmology
- Minimal Length Uncertainty Relation and gravitational quantum well
- Quantum Mechanics and the Generalized Uncertainty Principle
- The Big-Bang Singularity in the framework of a Generalized Uncertainty Principle
- Minimum Length Cutoff in Inflation and Uniqueness of the Action
- Harmonic oscillator with minimal length uncertainty relations and ladder operators
- The Bianchi IX model in Loop Quantum Cosmology
- Quantum suppression of the generic chaotic behavior close to cosmological singularities
- Corrections to the ns-levels of hydrogen atom in deformed space with minimal length
- Quantum Dynamics of the Taub Universe in a Generalized Uncertainty Principle framework
- Classical and Quantum Features of the Mixmaster Singularity
- On the Space-Time Uncertainty Relations of Liouville Strings and D Branes
- On the Covariance of the Mixmaster Chaoticity
- Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
- Generalized uncertainty principle in Bianchi type I quantum cosmology
- Influence of scalar fields on the approach to a cosmological singularity
- Exact solution of inflationary model with minimum length
- Is there chaos in string cosmology?
- Quantum cosmology with a minimal length
- A fundamental length as a candidate for dark energy: a DSR inspired FRW spacetime
- Minisuperspace dynamics in a generalized uncertainty principle framework
Cited by in corpus (12)
- Gauge Theories under Incorporation of a Generalized Uncertainty Principle
- Stability of the Kasner Universe in f(T) Gravity
- Extended GUP formulation and the role of momentum cut-off
- Towards a Cosmology with Minimal Length and Maximal Energy
- Chaotic universe in the z=2 Hovava-Lifshitz gravity
- Mixmaster universe in the z=3 deformed Hořava-Lifshitz gravity
- Semiclassical and quantum behavior of the Mixmaster model in the polymer approach for the isotropic Misner variable
- The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
- Generalized Uncertainty Principle theories and their classical interpretation
- Dynamics of the Mixmaster Universe in a non-commutative Generalized Uncertainty Principle framework
- On the emergence of a classical Isotropic Universe from a Quantum Bianchi Cosmology in the Jordan Frame
- Bianchi IX in the GUP approach