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A Complete Model of Cosmological Evolution of a Scalar Field with Higgs Potential and Euclidean Cycles

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Abstract

A revision of the author’s results concerning the possible existence of the so-called Euclidean cycles in cosmological evolution of a system of Higgs scalar fields is being performed. The assumption of a nonnegative velocity of the Universe expansion, which in certain cases contradicts the complete set of the Einstein equations, is removed. It is shown that in the cases where the effective energy of the system tends to zero, happens a smooth transition of the model to the range of negative values of the expansion rate, i.e., there is a transition to a collapsing stage rather than winding of the phase trajectories on the boundary of prohibited area. This process is studied with the help of numerical simulation methods for a model based on a classical scalar Higgs field.

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Notes

  1. Normally the case \(e=+1\) is considered, however, we will not restrict ourselves to that since the alternative model is also of interest, with \(\alpha<0\)

  2. We use \(G=\hbar=c=1\) everywhere in this paper, the signature of the metrics is \((-,-,-,+)\), the Ricci tensor is obtained by means of convolution of first and third indices.

  3. Let us agree on the notation: \(M_{11}(-,0,-)\); \(M_{12}(-,0,+)\); \(M_{21}(+,0,-)\) and \(M_{22}(+,0,+)\).

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ACKNOWLEDGMENTS

The author expresses his gratitude to Sergey Vernov who has informed the author on his research during the Winter School-Seminar ‘‘Petrov School 2018’’ in November, 2018.

Funding

>This work was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities.

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Authors and Affiliations

  1. Institute of Physics, Kazan Federal University, 420008, Kazan, Russia

    Yu. G. Ignat’ev & D. Yu. Ignat’ev

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  1. Yu. G. Ignat’ev
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  2. D. Yu. Ignat’ev
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Correspondence to Yu. G. Ignat’ev.

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Ignat’ev, Y.G., Ignat’ev, D.Y. A Complete Model of Cosmological Evolution of a Scalar Field with Higgs Potential and Euclidean Cycles. Gravit. Cosmol. 26, 29–37 (2020). https://doi.org/10.1134/S0202289320010065

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