Stability of the cosmological system of degenerated scalar charged fermions and Higgs scalar fields. I. Mathematical model of linear plane perturbations

Ignat'ev, Yu. G.

doi:10.48550/arxiv.2103.13866

Cited by 4 publications

(11 citation statements)

References 3 publications

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“…At the same time, in contrast to the works [18] - [19], the condition of the hard WKB approximation was not imposed in this paper, which allows considering also sufficiently long wavelengths:…”

Section: Unperturbed State Of a Homogeneous And Isotropic Cosmologica...mentioning

confidence: 99%

“…In particular, the class of such models was investigated by numerical simulation methods in the work [16], in which the possibility of controlling the stages of cosmological evolution using the parameters of scalarly charged fermions was shown. In [17], based on the study of degenerate systems of scalar-charged fermions with phantom interaction, it was suggested that Black Holes could form in the early Universe due to the gravitational-scalar instability of a cosmological system consisting of degenerate systems of scalarcharged fermions 1 In [18] - [19] based on the developed theory of instability of a one-component system of scalarly charged degenerate fermions with the singlet Higgs scalar interaction in the so-called hard WKB-approximation confirmed the assumption that such a system is unstable with respect to short-wavelength perturbations. These preliminary studies have shown the need for a comprehensive and deeper study of statistical systems of scalar charged particles.…”

Section: Introductionmentioning

confidence: 99%

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Gravitational - Scalar Instability of a Two-Component Degenerate System of Scalar Charged Fermions with Asymmetric Higgs Interaction

Ignat'ev

2022

Preprint

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Based on the previously formulated mathematical model of a statistical system with scalar interaction of fermions and the theory of gravitational-scalar instability of a cosmological model based on a two-component statistical system of scalar-charged degenerate fermions, a numerical model of the cosmological evolution of gravitational-scalar perturbations is constructed and specific examples of the development of instability are given. Some features of the instability's development are investigated depending on the nature of the behavior of the unperturbed cosmological model. It is shown that unstable modes can appear at very early stages of cosmological expansion or contraction, and the duration of the unstable phase is comparable to tens of Planck scales. In this case, however, a very significant increase in unstable modes is possible due to the redistribution of energy between the components of the scalar doublet.

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Section: Unperturbed State Of a Homogeneous And Isotropic Cosmologica...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gravitational - Scalar Instability of a Two-Component Degenerate System of Scalar Charged Fermions with Asymmetric Higgs Interaction

Ignat'ev

2022

Preprint

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“…Let us note the identity laws, which would be useful further and are valid for the Hamilton function (42):…”

Section: Invariant Canonical Formalism For Describing the Motion Of A...mentioning

confidence: 99%

“…by means of Dirac δ-function's properties and the explicit form of the Hamilton function (42), we find:…”

Section: Macroscopic Averages Of the Dynamic Functionsmentioning

confidence: 99%

“…This article also provides examples of numerical models of such systems, which radically differ in their behavior from the behavior of models based on vacuum scalar fields. Finally, in the works of one of the authors [42,43], a mathematical model of gravitational perturbations of the cosmological system of scalar charged fermions in the case of a scalar Higgs singlet (classical or phantom) was constructed and the stability of this cosmological model with respect to short-wave and scalar perturbations of the gravitational field was investigated. In these works, it was shown that the fermionic system is unstable in the early stages of cosmological expansion in the case of the classical Higgs interaction and is stable in the case of the phantom Higgs interaction.…”

Section: Introductionmentioning

confidence: 99%

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Cosmological Models Based on a Statistical System of Scalar Charged Degenerate Fermions and an Asymmetric Higgs Scalar Doublet

Ignat'ev,

Ignatyev

2021

Preprint

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On the basis of the general relativistic statistical and kinetic theory, a consistent closed cosmological model is formulated. It is based on a statistical system of scalar charged fermions interacting by means of classical and phantom scalar fields. Based on the study of the microscopic dynamics of scalar charged particles, within the framework of the Lagrangian as well as Hamiltonian formalism, a function of the dynamic mass of scalar charged particles was constructed and it was shown that for the consistency of the theory, it is necessary to remove the nonnegativity condition for this function. On the basis of the Lagrangian formalism, equations of gravitational and scalar fields with singular sources are formulated and microscopic conservation laws are obtained. Within the framework of the general relativistic kinetic theory, macroscopic equations of gravitational and scalar fields are formulated and macroscopic conservation laws are obtained. These equations' full correspondence to microscopic equations with singular sources is shown. Further, on the basis of the obtained equations, a cosmological model for a degenerate system of scalarly charged fermions is formulated. An exact solution of the constitutive equations for a degenerate scalar-charged plasma in the cosmological model is obtained, which made it possible to significantly simplify the original system of equations. On the basis of the obtained solution of the constitutive equations, two fundamentally different cosmological models are formulated, one of which has two types of singly scalarly charged fermions, while the second has one kind of fermions charged with two charges of various nature. A qualitative analysis of the obtained 6-dimensional dynamic system for a two-component model is carried out. It is shown that in such models, acceleration deceleration modes become possible at the later stages of the evolution of the Universe.

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Evolution of spherical perturbations in the cosmological environment of degenerate scalar-charged fermions with a scalar Higgs coupling

Ignat'ev

2023

Theor Math Phys

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A mathematical model is constructed for the evolution of spherical perturbations in a cosmological onecomponent statistical system of completely degenerate scalarly charged fermions with a scalar Higgs interaction. A complete system of self-consistent equations for small perturbations describing the evolution of spherical perturbations is constructed. Singular parts in perturbation modes corresponding to point mass and scalar charge are singled out. Systems of ordinary differential equations are obtained that describe the evolution of the mass and charge of a singular source, and systems of partial differential equations that describe the evolution of non-singular parts of perturbations. In this case, the coefficients of partial differential equations are described by solutions of evolutionary equations for mass and charge. The problem of spatially localized perturbations for solutions polynomial in the radial coordinate is reduced to a recurrent system of ordinary linear differential equations for the coefficients of these polynomials. The properties of solutions in the case of cubic polynomials are studied, in particular, it is shown that the radii of localization of gravitational and scalar perturbations coincide and evolve in proportion to the scale factor. Numerical modeling of the evolution of perturbations was carried out, in particular, it confirmed the exponential growth of the central mass of the perturbation, and also revealed the oscillatory nature of the evolution of the scalar charge.

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Stability of the cosmological system of degenerated scalar charged fermions and Higgs scalar fields. I. Mathematical model of linear plane perturbations

Cited by 4 publications

References 3 publications

Gravitational - Scalar Instability of a Two-Component Degenerate System of Scalar Charged Fermions with Asymmetric Higgs Interaction

Gravitational - Scalar Instability of a Two-Component Degenerate System of Scalar Charged Fermions with Asymmetric Higgs Interaction

Cosmological Models Based on a Statistical System of Scalar Charged Degenerate Fermions and an Asymmetric Higgs Scalar Doublet

Evolution of spherical perturbations in the cosmological environment of degenerate scalar-charged fermions with a scalar Higgs coupling

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