Behavior of the Universe anisotropy in a big-bounce cosmology

Abstract

We investigate the classical and quantum behavior of a Bianchi I model in the presence of a stiff matter contribution when the Vilenkin interpretation of the wave function of the Universe is taken into account. We study its evolution in the so-called polymer representation of quantum mechanics, in order to characterize the modifications that a discrete nature in the isotropic variable of the Universe induces on the morphology of the cosmological singularity. We demonstrate that in such a model the Big-Bang singularity is removed at a semiclassical level in favor of a Big-Bounce when a lattice on the isotropic variable is considered. Furthermore, the analysis of the mean values on the quantum degrees of freedom, \textit{i.e} the variables ${\beta }_{+},{\beta }_{-}$ in the Misner picture, and the investigation on the evolution of the wave packets show how the typical diverging behavior associated to the anisotropies of the Universe in proximity of the initial singularity disappears in our polymer modified scheme. Indeed, the anisotropies remain finite across the Big-Bounce and they assume a value that depends on the initial conditions fixed far from the turning point. Finally, we demonstrate that the proposed scenario can be extended, with a suitable choice of the configuration parameters, to the Bianchi IX cosmology and therefore it can be regarded as a paradigm for the generic cosmological model.

20 pages, 7 figures

References in corpus (6)

• Loop Quantum Cosmology: An Overview
• Polymer Quantum Mechanics and its Continuum Limit
• The Bianchi IX model in Loop Quantum Cosmology
• Hamiltonian and physical Hilbert space in polymer quantum mechanics
• Big-bounce cosmology from quantum gravity: The case of a cyclical Bianchi I universe
• Nonsingular cosmology from evolutionary quantum gravity

Cited by in corpus (8)

• Big-bounce and future time singularity resolution in Bianchi I: the projective invariant Nieh-Yan case
• An Overview on the Nature of the Bounce in LQC and PQM
• Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms
• WKB Approaches to Restore Time in Quantum Cosmology: Predictions and Shortcomings
• Study of the Inflationary Spectrum in the Presence of Quantum Gravity Corrections
• Bouncing cosmologies and stability analysis in symmetric teleparallel $f(Q)$ gravity
• Loop Quantum Cosmology of non-diagonal Bianchi models
• Polymer Quantization of the Isotropic Universe: comparison with the Bounce of Loop Quantum Cosmology