Statistical systems with phantom scalar interaction in gravitation theory. II. Macroscopic equations and cosmological models

Ignatyev, Yu. G.; Agathonov, A. A.; Ignatyev, D. Yu.

doi:10.1134/s0202289314040070

Cited by 28 publications

(32 citation statements)

References 7 publications

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“…On the basis of the stated mathematical model there was carried out numerical simulation of both degenerated Fermi systems and charge-symmetrical Boltzmann plasma consisting of scalar charged particles and antiparticles [9] [13]. These investigations revealed unique properties of the cosmological models which are based on the statistical systems of scalar charged particles with phantom scalar interaction.…”

Section: The Introductionmentioning

confidence: 99%

Qualitative and Numerical Analysis of the Cosmological Model with a Phantom Scalar Field

Ignatyev

2017

Russ Phys J

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In this paper we investigate the asymptotic behavior of the cosmological model based on phantom scalar field on the ground of qualitative analysis of the system of the cosmological model's differential equations and show that as opposed to models with classical scalar field, such models have stable asymptotic solutions with constant value of the potential both in infinite past and infinite future. We also develop numerical models of the cosmological evolution models with phantom scalar field in this paper. keywords: cosmological model, phantom scalar field, quality analysis, asymptotic behavior, numerical simulation, numerical gravitation. PACS: 04.20. Cv, 98.80.Cq, 96.50.S 52.27.Ny This work was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities. The IntroductionPreviously, there was created the cosmological model based on the statistical systems of scalar charged particle with interparticle phantom scalar interaction possessing negative kinetic energy of field [1] [8]. On the basis of the stated mathematical model there was carried out numerical simulation of both degenerated Fermi systems and charge-symmetrical Boltzmann plasma consisting of scalar charged particles and antiparticles [9] [13]. These investigations revealed unique properties of the cosmological models which are based on the statistical systems of scalar charged particles with phantom scalar interaction. However, since general results were obtained using numerical simulation methods, they hardly can be used for description of asymptotic properties of the corresponding models. Using combination of methods of the qualitative theory of ordinary differential equations and numerical integration of them, in [14]-[15] there were investigated the asymptotic properties of the standard cosmological model based on classic massive scalar field. Particularly, in these papers it is shown that the system of Einstein-Klein-Gordon equations for the homogenous space flat cosmological model has a single singular point corresponding to zero values of the scsalar field's potential and its derivative, where mentioned singular point can also be an attractive center or attractive focus, or attractive saddle. Besides, it was revealed a microscopic oscillating character of the invariant cosmological acceleration at approaching to the singular point with an average value corresponding to non-relativistic equation of state. In this paper we carry out similar investigation for the standard cosmological model based on phantom fields. In this model, as opposed to those, considered in [1] [13], we do not account contribution of the ordinary matter, i.e. we consider free phantom fields without a source.

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Section: The Introductionmentioning

confidence: 99%

Qualitative and Numerical Analysis of the Cosmological Model with a Phantom Scalar Field

Ignatyev

2017

Russ Phys J

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“…As a consequence of (24) we have to integrate the indicated system of equations, setting the constant in (24) equal to zero. This, in turn, means that Einstein's equation ( 22) can be used as an initial condition for determining, for example, the Hubble constant:…”

Section: Dynamic Equations For the Spatially Flat Friedmann Modelmentioning

confidence: 99%

“…Later, these studies were deepened to extend the theory of scalar, including phantom, fields to the sector of negative particle masses, degenerate Fermi systems, conformally invariant interactions, etc. [22], [23], [24], [25], [26]. The mathematical models of scalar fields constructed in this way were applied to the study of the cosmological evolution of systems of interacting particles and scalar fields, both classical and phantom types [27], [28], [29].…”

Section: Introductionmentioning

confidence: 99%

Complete cosmological model based on a asymmetric scalar Higgs doublet

Ignat'ev,

Kokh

2021

Preprint

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A study of a complete cosmological model based on an asymmetric scalar doublet represented by the classical and phantom scalar Higgs fields is carried out. At the same time, the assumption about the nonnegativity of the expansion rate of the Universe, which in some cases contradicts the complete system of Einstein's equations, was removed. A closed system of dynamic equations describing the evolution of the cosmological model is formulated, and the dependence of the topology of the Einstein -Higgs hypersurface of the 5-dimensional phase space of the dynamical system that determines the global properties of the cosmological model on the fundamental constants of the model is investigated. A qualitative analysis of the dynamical system of the corresponding cosmological model is carried out, asymptotic phase trajectories are constructed, and the results of numerical modeling are presented, illustrating various types of behavior of the cosmological model.

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“…The mathematical model of the scalar charged particles' statistical system based on the microscopic description and following procedure of transition to the kinetic theory was formulated in the previous articles [1,2]. The strict macroscopic consequences of the kinetic theory are the transport equations including the conservation law of a certain vector current corresponding to the microscopic conservation law in reactions of a certain fundamental charge e (if such a conservation law exists) -…”

Section: The Mathematical Model Of the Degenerated Scalar Charged Cos...mentioning

confidence: 99%

Numerical models of cosmological evolution of a degenerate Fermi-system of scalar charged particles

Ignatyev

Agathonov

2015

Gravit. Cosmol.

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Based on mathematical model of the statistical Fermi system with the interparticle interaction which was constructed in the previous articles, this work offers the construction and analysis of the numerical models of cosmological evolution of the single-component degenerated Fermi system of the scalar particles. The applied mathematics package Mathematica 9 is used for the numerical model construction.

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Statistical systems with phantom scalar interaction in gravitation theory. II. Macroscopic equations and cosmological models

Cited by 28 publications

References 7 publications

Qualitative and Numerical Analysis of the Cosmological Model with a Phantom Scalar Field

Qualitative and Numerical Analysis of the Cosmological Model with a Phantom Scalar Field

Complete cosmological model based on a asymmetric scalar Higgs doublet

Numerical models of cosmological evolution of a degenerate Fermi-system of scalar charged particles

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