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Complete cosmological model based on an asymmetric scalar Higgs doublet

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Abstract

We study a complete cosmological model based on an asymmetric scalar doublet represented by the classical and phantom scalar Higgs fields. Moreover, we remove the assumption that the expansion rate of the Universe is nonnegative, which contradicts the complete system of Einstein’s equations in several cases. We formulate a closed system of dynamical equations describing the evolution of the cosmological model and study the dependence of the topology of the Einstein–Higgs hypersurface of the five-dimensional phase space of the dynamical system that determines the global properties of the cosmological model based on the fundamental constants of the model. We analyze the dynamical system of the corresponding cosmological model qualitatively, construct asymptotic phase trajectories, and present numerical modeling results illustrating various types of behavior of the cosmological model.

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Notes

  1. By a complete cosmological model, we mean a model without nonnegativity condition (1) for the Hubble constant.

  2. The cosmological constant is renormalized according to (7) in these equations.

  3. For simplicity of notation in what follows, we omit their zero coordinates \(Z,z\) in the coordinates of these points.

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Funding

This research is performed in accordance with the Russian Government Program of Competitive Growth of Kazan Federal University.

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Authors and Affiliations

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

    Yu. G. Ignat’ev

  2. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, Kazan, Russia

    Yu. G. Ignat’ev & I. A. Kokh

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  1. Yu. G. Ignat’ev
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  2. I. A. Kokh
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Correspondence to Yu. G. Ignat’ev.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 207, pp. 133-176 https://doi.org/10.4213/tmf9987.

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Ignat’ev, Y.G., Kokh, I.A. Complete cosmological model based on an asymmetric scalar Higgs doublet. Theor Math Phys 207, 514–552 (2021). https://doi.org/10.1134/S0040577921040097

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