Bouncing Bianchi Models with Deformed Commutation Relations

TL;DR

This paper explores how deformed commutation relations can model quantum gravity effects in anisotropic Bianchi cosmological models, leading to bounce behaviors similar to loop quantum cosmology.

Contribution

It introduces modified Poisson brackets within DCRs that replicate LQC bounce dynamics for volume and anisotropy variables in Bianchi models.

Findings

Cosmological bounces observed in Bianchi I and II models.

Interaction between bounce and Kasner reflection in Bianchi II.

DCR framework effectively models quantum-gravity inspired bounces.

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.