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The big-bang singularity in the framework of a generalized uncertainty principle. (English) Zbl 1246.83238

Summary: We analyze the quantum dynamics of the Friedmann-Robertson-Walker Universe in the context of a Generalized Uncertainty Principle. Since the isotropic Universe dynamics resembles that of a one-dimensional particle, we quantize it with the commutation relations associated to an extended formulation of the Heisenberg algebra. The evolution of the system is described in terms of a massless scalar field taken as a relational time. We construct suitable wave packets and analyze their dynamics from a quasi-classical region to the initial singularity. The appearance of a non-singular dynamics comes out as far as the behavior of the probability density is investigated. Furthermore, reliable indications arise about the absence of a big-bounce, as predicted in recent issues of loop quantum cosmology.

MSC:

83F05 Relativistic cosmology
83C47 Methods of quantum field theory in general relativity and gravitational theory
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