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Article

Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative

1
PPGFis, CCE - Universidade Federal do Espírito Santo, Vitória 29075-910, ES, Brazil
2
Núcleo Cosmo-UFES & Departamento de Física - Universidade Federal do Espírito Santo, Vitória 29075-910, ES, Brazil
3
National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow 115409, Russia
4
Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
*
Author to whom correspondence should be addressed.
Professor Antônio Brasil Batista, one of the co-authors of this article, died on March 1, 2020, at the age of 81. Very active, giving regularly lectures at the PhD course of Physics at UFES (Brazil), participating in the supervision of Master and PhD students, he was interested in recent times, among other topics, in the applications and development of fractional derivatives, in particular in quantum cosmological systems, which is the subject of the present article, his last scientific contribution.
Universe 2020, 6(4), 50; https://doi.org/10.3390/universe6040050
Received: 23 January 2020 / Revised: 19 March 2020 / Accepted: 26 March 2020 / Published: 31 March 2020
(This article belongs to the Special Issue Quantum Models for Cosmology)
We study a quantization via fractional derivative of a nonminimal derivative coupling cosmological theory, namely, the Fab Four John theory. Its Hamiltonian version presents the issue of fractional powers in the momenta. That problem is solved here by the application of the so-called conformable fractional derivative. This leads to a Wheeler–DeWitt equation of second order, showing that a Bohm–de Broglie interpretation can be constructed. That combination of fractional quantization and Bohmian interpretation provides us a new quantization method, in which the quantum potential is the criterion to say if a quantum solution is acceptable or not to be further studied. We show that a wide range of solutions for the scale factor is possible. Among all of those, a bouncing solution analogous to the perfect fluid cosmology seems to deserve special attention. View Full-Text
Keywords: alternatives to inflationary models; modified gravity; quantum cosmology; quantization methods alternatives to inflationary models; modified gravity; quantum cosmology; quantization methods
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MDPI and ACS Style

Torres, I.; Fabris, J.C.; Piattella, O.F.; Batista, A.B. Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative. Universe 2020, 6, 50. https://doi.org/10.3390/universe6040050

AMA Style

Torres I, Fabris JC, Piattella OF, Batista AB. Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative. Universe. 2020; 6(4):50. https://doi.org/10.3390/universe6040050

Chicago/Turabian Style

Torres, Isaac, Júlio C. Fabris, Oliver F. Piattella, and Antônio B. Batista. 2020. "Quantum Cosmology of Fab Four John Theory with Conformable Fractional Derivative" Universe 6, no. 4: 50. https://doi.org/10.3390/universe6040050

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