Chaos and epoch structure in the deformed Mixmaster universe

TL;DR

This paper investigates how Planck-scale modifications, via polymer and GUP deformations, influence the chaotic dynamics of the Mixmaster universe, revealing that these corrections can either enhance or suppress chaos.

Contribution

It introduces a combined deformation framework affecting Mixmaster chaos, showing how quantum gravity effects alter epoch durations and chaotic behavior.

Findings

GUP corrections shorten Kasner epochs and increase wall collisions.

Polymer corrections prolong epochs and suppress bounces.

Deformation parameters modulate the strength of chaos.

Abstract

We study the dynamics of the Bianchi~IX (Mixmaster) universe under classical polymerization and generalized uncertainty principle (GUP) deformation of the Poisson brackets. Starting from the Misner Hamiltonian, we derive the effective equations of motion with both modifications and analyze the duration of Kasner epochs as a probe of dynamical behavior. Our results show that GUP corrections typically shorten the epochs, leading to more frequent wall collisions, whereas polymer corrections prolong them and suppress successive bounces. At leading order, the combined deformation produces an additive shift that interpolates between these two trends. While the billiard picture remains robust, the strength of Mixmaster chaos becomes sensitive to the deformation parameters. These results illustrate how Planck-scale corrections may either enhance or suppress cosmological chaos, offering a controlled framework for exploring early-universe dynamics.