Loop quantum cosmology of k=1 FRW: A tale of two bounces

Abstract

We consider the k=1 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology, paying special attention to the existence of an ambiguity in the quantization process. In spatially non-flat anisotropic models such as Bianchi II and IX, the standard method of defining the curvature through closed holonomies is not admissible. Instead, one has to implement the quantum constraints by approximating the connection via open holonomies. In the case of flat k=0 FRW and Bianchi I models, these two quantization methods coincide, but in the case of the closed $k$=1 FRW model they might yield different quantum theories. In this manuscript we explore these two quantizations and the different effective descriptions they provide of the bouncing cyclic universe. In particular, as we show in detail, the most dramatic difference is that in the theory defined by the new quantization method, there is not one, but two different bounces through which the cyclic universe alternates. We show that for a `large' universe, these two bounces are very similar and, therefore, practically indistinguishable, approaching the dynamics of the holonomy based quantum theory.

18 pages, 3 figures

References in corpus (18)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop quantum cosmology of k=1 FRW models
• Are loop quantum cosmos never singular?
• Loop Quantum Cosmology: An Overview
• Polymer Quantum Mechanics and its Continuum Limit
• Loop quantum cosmology and the k = - 1 RW model
• Closed FRW model in Loop Quantum Cosmology
• Anti-deSitter universe dynamics in LQC
• Is loop quantization in cosmology unique?
• A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology
• Quantum bounce and cosmic recall
• Exotic singularities and spatially curved Loop Quantum Cosmology
• On the Semiclassical Limit of Loop Quantum Cosmology
• The flat FRW model in LQC: the self-adjointness
• Elements of Loop Quantum Cosmology
• Alternative quantization of the Hamiltonian in isotropic loop quantum cosmology

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