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Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology

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Abstract

Inspired from the idea of minimally coupling of a real scalar field to geometry, we investigate the classical and quantum models of a flat energy-dependent FRW cosmology coupled to a perfect fluid in the framework of the scalar-rainbow metric gravity. We use the standard Schutz’ representation for the perfect fluid and show that under a particular energy-dependent gauge fixing, it may lead to the identification of a time parameter for the corresponding dynamical system. It is shown that, under some circumstances on the minisuperspace prob energy, the classical evolution of the of the universe represents a late time expansion coming from a bounce instead of the big-bang singularity. Then we go forward by showing that this formalism gives rise to a Schrödinger–Wheeler–DeWitt equation for the quantum-mechanical description of the model under consideration, the eigenfunctions of which can be used to construct the wave function of the universe. We use the resulting wave function in order to investigate the possibility of the avoidance of classical singularities due to quantum effects by means of the many-worlds and Bohmian interpretation of quantum cosmology.

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Notes

  1. With a straightforward calculation one can show that the variation of this term produces the boundary integral \(-\int _{\partial M}\sqrt{h}\epsilon h^{\alpha \beta }\delta g_{\alpha \beta ,\mu }n^{\mu }d^3y\), where \(n_{\mu }\) is the unit normal to \(\partial M\) and \(\epsilon =n_{\mu }n^{\mu }=\pm 1\), which is exactly equal to the variation of the second term in (7) but with different sign.

  2. It should be noted that while the fluid’s enthalpy depends on the rainbow function \(f_1\) through Eq. (14), its entropy seems to be free of such dependence. However, due to the Bekenstein-Hawking area law which is also applicable to the cosmological horizons, the entropy may also depend on the metric (and so to the rainbow) functions. In this situation, we may absorb all of such dependencies in variable S. This means that in the above discussions, by S we mean a metric dependence function. Finally, by applying of the canonical transformation (18), all information will be delivered to the variable T.

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Authors and Affiliations

  1. Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran

    M. Khodadi & K. Nozari

  2. Department of Physics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    B. Vakili

Authors
  1. M. Khodadi
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  2. K. Nozari
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  3. B. Vakili
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Correspondence to B. Vakili.

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Khodadi, M., Nozari, K. & Vakili, B. Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology. Gen Relativ Gravit 48, 64 (2016). https://doi.org/10.1007/s10714-016-2059-9

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