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Yu. G. Ignat'ev

Publications and source records attributed to Yu. G. Ignat'ev.

At least 37 records · Page 2Linked to original sources
arXiv2022

Complete cosmological evolution model of a classical scalar field with a Higgs potential. III. Features of phase trajectory flows

The flows of phase trajectories of cosmological models based on the vacuum classical Higgs field and their behavior on the Einstein-Higgs surface near singular points of a dynamical system are investigated by numerical simulation. The influence of the singular points on the process of phase flow splitting is shown and the efficiency of the Einstein-Higgs hypersurface application is demonstrated.

gr-qc↗
arXiv2022

Cosmological evolution of a statistical system of degenerate scalar-charged fermions with an asymmetric scalar doublet. I. Two-component system of assorted charges

Based on the mathematical model of a statistical system with scalar interaction of fermions formulated earlier, a cosmological model based on a two-component statistical system of scalar charged degenerate fermions interacting with an asymmetric scalar doublet, canonical and phantom scalar fields, is investigated. The asymptotic and limiting properties of the cosmological model are investigated, and it is shown that among all models there is a class of models with a finite lifetime. The asymptotic behavior of models near the corresponding singularities is investigated and numerical implementations of such models are constructed.

gr-qc↗
arXiv2022

Cosmological evolution of a statistical system of degenerate scalar charged fermions with an asymmetric scalar doublet. II. One-component system of doubly charged fermions

Based on the previously formulated mathematical model of a statistical system with scalar interaction of fermions, a cosmological model based on a one-component statistical system of doubly scalar charged degenerate fermions interacting with an asymmetric scalar doublet-canonical and phantom scalar fields-is studied. The connection 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 a 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 presented 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 the expansion phase. The time interval of the transition between phases is accompanied by oscillations of the canonical scalar field.

gr-qc↗
arXiv2022

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

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.

gr-qc↗
arXiv2021

Complete cosmological evolution model of a classical scalar field with a higgs potential. II. Numerical simulation

A complete cosmological evolution model of the classical scalar field with a Higgs potential is studied and simulated on a computer without the assumption that the Hubble constant is nonnegative. It is shown that with most initial conditions, the cosmological model goes from the expansion stage to the compression stage. Thus, cosmological models based on the classical Higgs field are unstable to finite perturbations.

gr-qc↗
arXiv2021

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

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.

gr-qc↗
arXiv2021

Complete model of cosmological evolution of a classical scalar field with the Higgs potential. I. Analysis of the model

A complete model of cosmological evolution of a classical scalar field with the Higgs potential is studied and simulated on a computer without assumption that the Hubble constant is nonnegative. The corresponding dynamical system is qualitatively analyzed and the Einstein-Higgs hypersurfaces the topology of which determines the global properties of the phase trajectories of the cosmological model are classified.

physics.gen-ph↗
arXiv2021

Complete cosmological model based on a asymmetric scalar Higgs doublet

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.

gr-qc↗
arXiv2021

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

A mathematical model of the evolution of plane perturbations in the cosmological statistical system of completely degenerated scalar-charged fermions with the Higgs scalar interaction is formulated. A complete closed system of differential equations describing the unperturbed state of a homogeneous and isotropic system and a system of self-consistent equations describing the evolution of small perturbations are constructed.

gr-qc↗
arXiv2021

The Stability of the Cosmological System of Degenerate Scalar Charged Fermions and Higgs Scalar Fields. II. The Evolution of Short-Wave Perturbations

A mathematical model of the evolution of plane perturbations in the cosmological statistical system of completely degenerate scalar-charged fermions with Higgs scalar interaction for short-wave perturbations is formulated. These disturbance modes have been found and investigated. It is shown that in such a model an additional oscillation mode arises, which is associated directly with degenerate fermions, in which monotonically decreasing and increasing perturbations of the metric exist. In this case, there is such a time instant in the system that the potential of the scalar field, together with the energy density, tends to infinity. In this regard, an assumption is made about a possible mechanism for the formation of dark matter condensates.

gr-qc↗
arXiv2020

Kinetic equations for ultrarelativistic particles in a Robertson-Walker Universe and isotropization of relict radiation by gravitational interactions

Kinetic equations for ultrarelativistic particles with due account of gravitational interactions with massive particles in the Robertson-Walker universe are obtained. On the basis of an exact solution of the kinetic equations thus obtained, a conclusion is made as to the high degree of the uniformity of the relict radiation on scales with are less than $10'$.

gr-qc↗
arXiv2020

Short-wave Approximation For Macroscopic Cosmology with Higgs Scalar Field

Based on the macroscopic equations of cosmological evolution obtained earlier by the Author, a closed system of macroscopic Einstein equations in the short-wave approximation for perturbations of the scalar Higgs and gravitational fields has been obtained and examined. The obtained exact solutions of macroscopic equations are determined by three microscopic parameters, depending on the spectrum of perturbations.

gr-qc↗
arXiv2020

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

The revision of the Author's results with respect to possibility of existence of the so-called Euclidian cycles in cosmological evolution of a system of Higgs scalar fields has been performed. The assumption of non-negativity of the Universe's extension velocity, which contradicts in certain cases to complete system of Einstein equations, has been removed. It has been shown that in cases when effective energy of the system tends to zero, a smooth transition of the model to the range of negative values of the extension velocity occurs, i.e. it occurs the transition to collapse stage rather than winding of the phase trajectories on the boundary of prohibited area. This process has been researched with a help of numerical simulation methods for the model based on classical scalar Higgs field.

gr-qc↗
arXiv2020

The Method of Self-Consistent Field and Macroscopical Einstein Equations for the Early Universe

The complete theory of cosmological evolution's macroscopic description is constructed with a help of self-consistent field. The theory includes a subsystem of linear equations of perturbations' evolution and nonlinear macroscopic Einstein equations and equations of a scalar field. We provide examples of system's solution which show the principal difference of the cosmological models of the early Universe built on homogenous and locally fluctuating scalar fields. {\bf Keywords}: macroscopic gravitation, self-consistent field, cosmological model, scalar fields, averaging of local fluctuations, asymptotical behavior, cosmological singularity.

gr-qc↗
arXiv2019

The self-consistent field method and the macroscopic universe consisting of a fluid and a black holes

The article discusses and substantiates a self-consistent approach to the macroscopic description of systems with gravitational interaction. Corrections to the equation of state of the fluid are found based on macroscopic Einstein equations which were obtained by averaging over microscopic spherically symmetric metric fluctuations created by the primary Black Holes in a fluid medium. It is shown that these corrections are effectively equivalent to addition of a fluid to the system with the equation of state $p=-\varepsilon$. In addition, it is shown that, in this case, the mass of Black Holes can grow at a modern stage of evolution to very large values.

gr-qc↗
arXiv2019

Qualitative and Numerical Analysis of a Cosmological Model Based on an Asymmetric Scalar Doublet with Minimal connections. IV. Numerical Modeling and Types of Behavior of the Model

On the basis of a qualitative and numerical analysis of a cosmological model based on an asymmetric scalar doublet of nonlinear, minimally interacting scalar fields -- one classical and one phantom, peculiarities of the behavior of the model near zero energy hypersurfaces have been revealed. Numerical models have been constructed, in which the dynamical system has limit cycles on the zero-energy hypersurfaces. Three types of behavior of the cosmological model have been distinguished, configured by the fundamental constants of the scalar fields and the initial conditions. It is shown that over a wide sector of values of the fundamental constants and initial conditions, the cosmological models have a tendency to adhere to the zero-energy hypersurfaces corresponding to 4-dimensional Euclidean space.

gr-qc↗