The Mixmaster Universe in a generalized uncertainty principle framework

The Bianchi IX cosmological model is analyzed in a generalized uncertainty principle framework. The Arnowitt–Deser–Misner reduction of the dynamics is performed and a time-coordinate, namely the volume of the Universe, naturally arises. Such a variable is treated in the ordinary way while the anisotropies (the physical degrees of freedom) are described by a deformed Heisenberg algebra. The analysis of the model (passing through Bianchi I and II) is performed at classical level by studying the modifications induced on the symplectic geometry by the deformed algebra. We show that the Universe cannot isotropize because of the deformed Kasner dynamics, 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. Furthermore, no reflection law can be in general obtained since the Bianchi II model is no longer analytically integrable. This way, the deformed Mixmaster Universe can be still considered as a chaotic system.