Quantum dynamics of the Taub universe in a generalized uncertainty principle framework

Abstract

The implications of a generalized Uncertainty principle on the Taub cosmological model are investigated. The model is studied in the Arnowitt-Deser-Misner reduction of the dynamics and therefore a time variable is ruled out. Such a variable is quantized in a canonical way and the only physical degree of freedom of the system (related to the universe anisotropy) is quantized by means of a modified Heisenberg algebra. The analysis is performed at both the classical and quantum level. In particular, at quantum level, the motion of wave packets is investigated. The two main results obtained are as follows: (i) The classical singularity is probabilistically suppressed. The universe exhibits a stationary behavior and the probability amplitude is peaked in a determinate region. (ii) The generalized uncertainty principle wave packets provide the right behavior in the establishment of a quasi-isotropic configuration for the universe.