The Bianchi IX model in Loop Quantum Cosmology

Abstract

The Bianchi IX model has been used often to investigate the structure close to singularities of general relativity. Its classical chaos is expected to have, via the BKL scenario, implications even for the approach to general inhomogeneous singularities. Thus, it is a popular model to test consequences of modifications to general relativity suggested by quantum theories of gravity. This paper presents a detailed proof that modifications coming from loop quantum gravity lead to a non-chaotic effective behavior. The way this is realized, independently of quantization ambiguities, suggests a new look at initial and final singularities.

41 pages, 3 figures, revtex4

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• Loop Quantum Cosmology
• Loop quantum cosmology of Bianchi type IX models
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Spherically Symmetric Quantum Geometry: Hamiltonian Constraint
• Homogeneous Loop Quantum Cosmology: The Role of the Spin Connection
• Genericness of Big Bounce in isotropic loop quantum cosmology
• Loop Quantum Gravity and the Cyclic Universe
• Hybrid Quantization: From Bianchi I to the Gowdy Model
• Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
• Quantum gravitational Kasner transitions in Bianchi-I spacetime
• Nonsingular Black Holes and Degrees of Freedom in Quantum Gravity
• Classical and Quantum Features of the Mixmaster Singularity
• Numerical simulations of loop quantum Bianchi-I spacetimes
• Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
• Genericness of inflation in isotropic loop quantum cosmology
• Primordial Density Perturbation in Effective Loop Quantum Cosmology
• Absence of pre-classical solutions in Bianchi I loop quantum cosmology
• Wave functions for the Schwarschild black hole interior
• Effective Hamiltonian for Isotropic Loop Quantum Cosmology
• Singularity avoidance in a quantum model of the Mixmaster universe
• The Volume Operator in Spherically Symmetric Quantum Geometry
• Coordinate time dependence in Quantum Gravity
• Perturbative Degrees of Freedom in Loop Quantum Gravity: Anisotropies
• An Overview on the Nature of the Bounce in LQC and PQM
• Inflationary scalar spectrum in loop quantum cosmology
• Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations
• Absence of the Kasner singularity in the effective dynamics from loop quantum cosmology
• Degenerate Configurations, Singularities and the Non-Abelian Nature of Loop Quantum Gravity
• Elements of Loop Quantum Cosmology
• Singularity-free and non-chaotic inhomogeneous Mixmaster in polymer representation for the volume of the universe
• On Energy Conditions and Stability in Effective Loop Quantum Cosmology
• The Mixmaster Universe in a generalized uncertainty principle framework
• Behavior of the Universe anisotropy in a big-bounce cosmology
• Loop quantum cosmology of Bianchi IX: Effective dynamics
• The Early Universe in Loop Quantum Cosmology
• Semiclassical and quantum behavior of the Mixmaster model in the polymer approach for the isotropic Misner variable
• Anisotropic loop quantum cosmology with self-dual variables
• Anisotropic cosmology and inflation from tilted Bianchi IX model
• Thermodynamics in Loop Quantum Cosmology
• Quantum Geometry and its Implications for Black Holes
• Semiclassical and quantum behavior of the Mixmaster model in the polymer approach
• Quantum gravity might restrict a cyclic evolution
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Tachyon field in loop quantum cosmology: An example of traversable singularity
• Violation of Strong Energy Condition in Effective Loop Quantum Cosmology
• Universe scenarios from loop quantum cosmology
• Chaos Removal in the $R+q{R}^2$ gravity: the Mixmaster model
• Perturbation theory in covariant canonical quantization
• Fate of Mixmaster Chaos in a Deformed Algebra framework
• The role of spatial curvature in constraining the Universe anisotropies across a Big Bounce
• Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe
• Appearance of classical Mixmaster Universe from the No-Boundary Quantum State
• Quantum Big-Bounce as a phenomenology of RQM in the Mini-superspace
• Dynamical Horizon Entropy Bound Conjecture in Loop Quantum Cosmology
• Semiclassical study of the Mixmaster model: the quantum Kasner map