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Classical and quantum Hořava-Lifshitz cosmology in a minisuperspace perspective. (English) Zbl 1271.83072

Summary: We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology in the framework of the gravity theory proposed by Hořava, the so-called Hořava-Lifshitz theory of gravity. Beginning with the ADM representation of the action corresponding to this model, we construct the Lagrangian in terms of the minisuperspace variables and show that in comparison with the usual Einstein-Hilbert gravity, there are some correction terms coming from the Hořava theory. Either in the matter free or in the case when the considered universe is filled with a perfect fluid, the exact solutions to the classical field equations are obtained for the flat, closed and open FRW model and some discussions about their possible singularities are presented. We then deal with the quantization of the model in the context of the Wheeler-DeWitt approach of quantum cosmology to find the cosmological wave function. We use the resulting wave functions to investigate the possibility of the avoidance of classical singularities due to quantum effects.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83F05 Relativistic cosmology
83C45 Quantization of the gravitational field
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C75 Space-time singularities, cosmic censorship, etc.
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