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Cosmological Evolution of a Statistical System of Degenerate Scalarly Charged Fermions with an Asymmetric Scalar Doublet. II. One-Component System of Doubly Charged Fermions\({}^{a}\)

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Abstract

Based on the previously formulated mathematical model of a statistical system with scalar interaction of fermions, a cosmological model is studied, based on a one-component statistical system of doubly scalarly charged degenerate fermions interacting with an asymmetric scalar doublet of canonical and phantom scalar fields. A relationship of the presented model with previously studied models based on one-component and two-component fermion systems is investigated. The asymptotic and limiting properties of the cosmological model are investigated, it is shown that among all models there is a class of models with finite lifetime. The asymptotic behavior of models near the corresponding singularities is investigated, a qualitative analysis of the corresponding dynamical system is carried out, and numerical implementations of such models are constructed. Based on numerical integration, it is shown that in the present model there can be transitions from a stable asymptotically vacuum state with a zero canonical field and a constant phantom field, corresponding to the phase of cosmological compression, to a symmetric state corresponding to an expansion phase. The time interval of the transition between these phases is accompanied by oscillations of the canonical scalar field.

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Notes

  1. In this article, we use the metric signature \((---+)\), and the Ricci tensor is determined by convolution of the first and third indices of the curvature tensor (see, for example, [16]).

  2. For a single-component system of degenerate fermions, see [19, 20], and for a multicomponent system, see [14].

  3. See a discussion on this issue in [15].

  4. Singlets with both canonical and phantom scalar fields were studied in the \(\mathfrak{M}_{00}\) and \(\mathfrak{M}_{0}\) models.

  5. This state is not allowed in all cases of model parameters, see below.

  6. See, e.g., [22].

  7. We talked about that in Subsection 3.2.1.

  8. Numerical integration gives the results \(\Phi(\mp\infty)=10^{-15}{-}10^{-14}\).

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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, Kremlyovskaya St. 18, Kazan, 420008, Russia

    Yu. G. Ignat’ev & D. Yu. Ignatyev

  2. Lobachevsky Institute of Mathematics and Mechanics, Kazan Federal University, Kremlyovskaya St. 18, Kazan, 420008, Russia

    A. A. Agathonov

Authors
  1. Yu. G. Ignat’ev
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  2. A. A. Agathonov
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  3. D. Yu. Ignatyev
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Correspondence to Yu. G. Ignat’ev.

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aBasically, quasars, such as, for example, the supermassive BH SDS J140821. 67+025733.2 at the center of the quasar SDSS J140821, having a mass of \(1.96\times 10^{11}M_{\odot}\).

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Ignat’ev, Y.G., Agathonov, A.A. & Ignatyev, D.Y. Cosmological Evolution of a Statistical System of Degenerate Scalarly Charged Fermions with an Asymmetric Scalar Doublet. II. One-Component System of Doubly Charged Fermions\({}^{a}\). Gravit. Cosmol. 28, 10–24 (2022). https://doi.org/10.1134/S0202289322010066

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