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A phase space description of the FLRW quantum cosmology in Hořava–Lifshitz type gravity

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Abstract

Quantum cosmology of the Friedmann–Lemaître–Robertson–Walker model with cosmological constant in the Hořava–Lifshitz type gravity is studied in the phase space by means of the Wigner function. The modification of the usual general relativity description by the Hořava–Lifshitz type gravity induces a new scenario for the origin of the Universe with an embryonic era where the Universe can exist classically before the tunneling process takes place and which gives rise to the current evolution of the Universe. The Wigner functions corresponding to the Hartle–Hawking, Vilenkin and Linde boundary conditions are obtained by means of numerical calculations. In particular three cases were studied for the potential of the Wheeler–DeWitt equation: tunneling barrier with and without embryonic era and when the potential barrier is not present. The quantum behavior of these three cases are analyzed using the Wigner function for the three boundary conditions considered.

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Acknowledgements

We want to thank the referees for their comments and suggestions which allowed us to improve this work. The work of R. C., H. G.-C. and F. J. T. was partially supported by SNI-México, CONACyT research Grant: 128761. In addition R. C. and F. J. T. were partially supported by COFAA-IPN and by SIP-IPN Grants 20171168, 20171100, 20180735, 20180741, 20194924 and 20195330. We are indebted to Héctor Uriarte for all his help in the elaboration of the figures presented in the paper.

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  1. Departamento de Física, Escuela Superior de Física y Matemáticas del Instituto Politécnico Nacional, Unidad Adolfo López Mateos, Edificio 9, 07738, Mexico City, Mexico

    Rubén Cordero & Francisco J. Turrubiates

  2. Departamento de Física, Centro de Investigación y de Estudios Avanzados del IPN, P.O. Box 14-740, 07000, Mexico City, Mexico

    Hugo García-Compeán

  3. División de Ciencias e Ingenierías, Departamento de Física, Universidad de Guanajuato, Campus León, Loma del Bosque No. 103, Fraccionamiento Lomas del Campestre, León, Guanajuato, Mexico

    Hugo García-Compeán

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  1. Rubén Cordero
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Cordero, R., García-Compeán, H. & Turrubiates, F.J. A phase space description of the FLRW quantum cosmology in Hořava–Lifshitz type gravity. Gen Relativ Gravit 51, 138 (2019). https://doi.org/10.1007/s10714-019-2627-x

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