Chaos and epoch structure in the deformed Mixmaster universe
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.
Keywords
Cite
@article{arxiv.2605.12173,
title = {Chaos and epoch structure in the deformed Mixmaster universe},
author = {Babak Vakili},
journal= {arXiv preprint arXiv:2605.12173},
year = {2026}
}
Comments
26 pages, 2 figures, to appear in IJGMMP, This is the second part of a two-part article, the first part of which, titled "Classical Polymerization of the Bianchi I Model with Deformed Poisson Structure" has already been uploaded to the arXiv with ID number: 2510.06628 [gr-qc]