A quantum gravity extension to the Mixmaster dynamics

Abstract

In the loop quantum cosmology effective dynamics for the vacuum Bianchi type I and type IX space-times, a non-singular bounce replaces the classical singularity. The bounce can be approximated as an instantaneous transition between two classical vacuum Bianchi I solutions, with simple transition rules relating the solutions before and after the bounce. These transition rules are especially simple when expressed in terms of the Misner variables: the evolution of the mean logarithmic scale factor is reversed, while the shape parameters are unaffected. As a result, the loop quantum cosmology effective dynamics for the vacuum Bianchi IX space-time can be approximated by a sequence of classical vacuum Bianchi I solutions, following the usual Mixmaster transition maps in the classical regime, and undergoing a bounce with this new transition rule in the Planck regime.

6 pages

References in corpus (10)

• Quantum Nature of the Big Bang: Improved dynamics
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
• Loop Quantization of Vacuum Bianchi I Cosmology
• Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
• The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
• Quantum suppression of the generic chaotic behavior close to cosmological singularities
• Quantum gravitational Kasner transitions in Bianchi-I spacetime
• Classical and Quantum Features of the Mixmaster Singularity
• The loop quantum cosmology bounce as a Kasner transition

Cited by in corpus (10)

• An Overview on the Nature of the Bounce in LQC and PQM
• The singularity in mimetic Kantowski-Sachs cosmology
• A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories
• Polymer representation of the Bianchi IX Cosmology in the Misner variables
• Observational constraints on anisotropies for bouncing alternatives to inflation
• Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe
• Numerics of Bianchi type II and type IX spacetimes in effective loop quantum cosmology
• Ekpyrosis in Quantum Gravitational Anisotropic Bouncing Models
• Weyl Curvature Hypothesis in light of Quantum Backreaction at Cosmological Singularities or Bounces
• Semiclassical study of the Mixmaster model: the quantum Kasner map