Bianchi IX in the GUP approach

TL;DR

This paper investigates the Bianchi IX cosmological model within a generalized uncertainty principle framework, revealing that anisotropies persist, the universe's dynamics are altered, and classical reflection laws are not applicable due to non-integrability.

Contribution

It introduces a novel analysis of Bianchi IX in GUP, showing how deformed algebra affects anisotropy evolution and integrability, which was not previously explored.

Findings

Universe cannot isotropize due to deformed Kasner dynamics.

The allowed domain becomes asymptotically stationary.

No reflection law can be derived because of non-integrability.

Abstract

The Bianchi IX cosmological model (through Bianchi I and II) is analyzed in the framework of a generalized uncertainty principle. In particular, the anisotropies of the Universe are described by a deformed Heisenberg algebra. Three main results are in order. (i) The Universe can not isotropize because of the deformed Kasner dynamics. (ii) The triangular allowed domain is asymptotically stationary with respect to the particle (Universe) and its bounces against the walls are not interrupted by the deformed effects. (iii) No reflection law can be in obtained since the Bianchi II model is no longer analytically integrable.