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Dilaton Quantum Cosmology with a Schrödinger-like Equation

Brazilian Journal of Physics volume 42, pages475–481(2012)Cite this article

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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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Fig. 1

Notes

  1. 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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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
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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) doi:10.1007/s13538-012-0105-y

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Keywords

  • Quantum cosmology
  • Gravitation
  • Quantum gravity