Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-05-18
Phys.Rev.D84:044003,2011
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages, 3 figures
Scientific paper
10.1103/PhysRevD.84.044003
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.
Corichi Alejandro
Karami Asieh
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