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Dilaton Quantum Cosmology with a Schrödinger-like Equation

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Abstract

A quantum cosmological model with radiation and a dilaton scalar field is analyzed. The Wheeler–DeWitt equation in the minisuperspace induces a Schrödinger equation, which can be solved. An explicit wavepacket is constructed for a particular choice of the ordering factor. A consistent solution is possible only when the scalar field is a phantom field. Moreover, although the wavepacket is time-dependent, a Bohmian analysis allows to extract a bouncing behavior for the scale factor.

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Notes

  1. It can already be stated that the solutions are not equivalent to the expectation values found before, a consequence of the absence of unitarity: when the wavepacket is unitary, the Bohmian trajectories reproduces the expectation values.

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Acknowledgements

We thank the CNPq for partial financial support. JM and PVM were also supported by the grant CERN/FP/116373/2010. PVM is grateful to the CENTRA-IST for financial assistance. He also wants to thank the hospitality of the UFES, where this work was completed.

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Authors and Affiliations

  1. Departamento de Física, Universidade Federal do Espírito Santo, Vitória, Espirito Santo, Brazil

    J. C. Fabris

  2. ICRA, Centro Brasileiro de Pesquisas Físicas, Urca, Rio de Janeiro, Brazil

    F. T. Falciano & N. Pinto-Neto

  3. Departamento de Física, Universidade da Beira Interior, Covilhã, Portugal

    J. Marto & P. Vargas Moniz

Authors
  1. J. C. Fabris
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  2. F. T. Falciano
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  3. J. Marto
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  4. N. Pinto-Neto
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  5. P. Vargas Moniz
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Correspondence to J. C. Fabris.

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Fabris, J.C., Falciano, F.T., Marto, J. et al. Dilaton Quantum Cosmology with a Schrödinger-like Equation. Braz J Phys 42, 475–481 (2012). https://doi.org/10.1007/s13538-012-0105-y

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  • DOI: https://doi.org/10.1007/s13538-012-0105-y

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