Barca, G. orcid.org/0000-0001-6445-9193 and Giovannetti, E. orcid.org/0000-0002-0271-5822 (2025) Fate of Mixmaster chaos in a deformed algebra framework. Universe, 11 (2). 63. ISSN 2218-1997
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 in 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
Keywords: | Mixmaster universe; alternative quantum mechanics; non-commutativity; chaos |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematical and Physical Sciences |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 Mar 2025 14:46 |
Last Modified: | 17 Mar 2025 14:46 |
Status: | Published |
Publisher: | MDPI AG |
Refereed: | Yes |
Identification Number: | 10.3390/universe11020063 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:224516 |