Bouncing Bianchi Models with Deformed Commutation Relations
arXiv:2507.01678 · doi:10.1103/fwfy-gtgx
Abstract
We study the anisotropic Bianchi I and Bianchi II models in vacuum in the framework of deformed commutation relations (DCRs). Working in a parametrisation of the spatial metric by a volume and two anisotropy variables, we propose modified Poisson brackets that for the volume alone reproduce the bounce dynamics of effective loop quantum cosmology (LQC), with additional modifications for anisotropy degrees of freedom. We derive effective Friedmann equations and observe cosmological bounces both in Bianchi I and Bianchi II. For Bianchi II, we find that the cosmological bounce now interacts with the usual reflection seen in the Kasner indices in various interesting ways, in close similarity again with what had been seen in LQC. This suggests that the DCR framework could model more general quantum-gravity inspired bounce scenarios in a relatively straightforward way.
13 pages, 5 figures. New upload to match published version. Includes the Mathematica notebook containing the code used to numerically solve the deformed Bianchi II model and generate Fig. 4
References in corpus (22)
- Loop Quantum Cosmology: A Status Report
- Minimal Length Scale Scenarios for Quantum Gravity
- Loop Quantum Cosmology
- Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
- The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
- Relational Observables in Gravity: a Review
- Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
- Emergent de Sitter epoch of the quantum Cosmos
- Critical evaluation of common claims in loop quantum cosmology
- The loop quantum cosmology bounce as a Kasner transition
- Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms
- Generalised effective cosmology from group field theory
- Quantum empty Bianchi I spacetime with internal time
- A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories
- Emergent Universe Model from Modified Heisenberg Algebra
- Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity
- n-dimensional non-commutative GUP quantization and application to the Bianchi I model
- Gauge-invariant bounce from loop quantum gravity
- Generalized Uncertainty Principle theories and their classical interpretation
- Dynamics of the Mixmaster Universe in a non-commutative Generalized Uncertainty Principle framework
- Fate of Mixmaster Chaos in a Deformed Algebra framework
- Relativistic modeling of cosmological structures with Bianchi IX spacetimes