We analyze the quantum dynamics of the Bianchi Type IX model, as described in the so-called polymer representation of quantum mechanics, to characterize the modifications that a discrete nature in the anisotropy variables of the Universe induces on the morphology of the cosmological singularity. We first perform a semiclassical analysis, to be regarded as the zeroth-order approximation of a WKB approximation of the quantum dynamics, and demonstrate how the features of polymer quantum mechanics are able to remove the chaotic properties of the Bianchi IX dynamics. The resulting evolution towards the cosmological singularity overlaps the one induced, in a standard Einsteinian dynamics, by the presence of a free scalar field. Then, we address the study of the full quantum dynamics of this model in the polymer representation and analyze the two cases in which the Bianchi IX spatial curvature does not affect the wave-packet behavior, as well as the instance for which it plays the role of an infinite potential confining the dynamics of the anisotropic variables. The main development of this analysis consists of investigating how, differently from the standard canonical quantum evolution, the high quantum number states are not preserved arbitrarily close to the cosmological singularity. This property emerges as a consequence, on one hand, of the no-longer-chaotic features of the classical dynamics (on which the Misner analysis is grounded), and, on the other hand, of the impossibility of removing the quantum effect due to the spatial curvature. In the polymer picture, the quantum evolution of the Bianchi IX model remains always significantly far from the semiclassical behavior, as far as both the wave-packet spread and the occupation quantum numbers are concerned. As a result, from a quantum point of view, the mixmaster dynamics loses any predictivity characterization for the discrete nature of the Universe's anisotropy. © 2013 American Physical Society.
|Titolo:||Semiclassical and quantum behavior of the mixmaster model in the polymer approach|
|Data di pubblicazione:||2013|
|Appare nelle tipologie:||1.1 Articolo in rivista|