Fate of Mixmaster Chaos in a Deformed Algebra framework

TL;DR

This paper investigates how deformed algebra frameworks inspired by quantum gravity affect the chaotic behavior of the Mixmaster universe, showing that chaos can be suppressed or eliminated depending on the deformation sign.

Contribution

It introduces a classical limit implementation of deformed commutation relations in Bianchi IX models and derives the modified BKL map to analyze chaos suppression.

Findings

Deformations can remove the initial singularity similar to Loop Quantum Cosmology.

Depending on the deformation sign, chaos is either suppressed or eliminated.

The modified dynamics lead to either oscillations or a final Kasner solution, ending chaos.

Abstract

We analyze the anisotropic Bianchi models, and in particular the Bianchi Type IX known as the Mixmaster universe, where the Misner anisotropic variables obey Deformed Commutation Relations inspired by Quantum Gravity theories. We consider three different deformations, two of which have been able to remove the initial singularity similarly to Loop Quantum Cosmology when implemented to the single volume variable. Here, the two-dimensional Algebras naturally implement a form of Non-Commutativity between the space variables that affects the dynamics of the anisotropies. In particular, we implement the modifications in their classical limit, where the Deformed Commutators become Deformed Poisson Brackets. We derive the modified Belinskii-Khalatnikov-Lifshitz map in all the three cases, and we study the fate of the chaotic behavior that the model classically presents. Depending on the sign of the deformation, the dynamics will either settle into oscillations between two almost-constant angles, or stop reflecting after a finite number of iterations and reach the singularity as one last simple Kasner solution. In either case, chaos is removed.