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Bouncing Bianchi models with deformed commutation relations

Gabriele Barca1,2,* and Steffen Gielen1,†

  • *Contact author: gabriele_barca001@ehu.eus
  • †Contact author: s.c.gielen@sheffield.ac.uk
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Phys. Rev. D 112, 086014 – Published 24 October, 2025

DOI: https://doi.org/10.1103/fwfy-gtgx

Abstract

We study the anisotropic Bianchi I and Bianchi II models in vacuum in the framework of deformed commutation relations. Working in a parametrization 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, with additional modifications for anisotropy degrees of freedom. We derive effective Friedmann equations and observe cosmological bounces in both 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 loop quantum cosmology. This suggests that the deformed commutation relation framework could model more general quantum-gravity-inspired bounce scenarios in a relatively straightforward way.

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Phys. Rev. D 112, 086014– Published 24 October, 2025
  • Received 8 July 2025
  • Accepted 27 September 2025
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