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.

arXiv comment20 pages, 7 figures

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• Polymer Quantum Mechanics and its Continuum Limit
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• Hamiltonian and physical Hilbert space in polymer quantum mechanics
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Cited by in corpus (12)

• 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
• Semi-classical and quantum analysis of the isotropic Universe in the polymer paradigm
• 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
• Polymer representation of the Bianchi IX Cosmology in the Misner variables
• Semiclassical and quantum behavior of the Mixmaster model in the polymer approach for the isotropic Misner variable
• Bianchi I model as a prototype for a cyclical Universe
• Loop Quantum Cosmology of non-diagonal Bianchi models
• Polymer Quantization of the Isotropic Universe: comparison with the Bounce of Loop Quantum Cosmology