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Yu. G. Ignat'ev

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

52 records · Page 3Linked to original sources
arXiv2019

Qualitative and Numerical Analysis of a Cosmological Model Based on an Asymmetric Scalar Doublet with Minimal Couplings. I. Qualitative Analysis of the Model

A qualitative analysis of a cosmological model based on the asymmetric scalar doublet classical + phantom scalar field with minimal interaction is performed. It is shown that depending on the parameters of the model, the corresponding dynamical system can have 1, 3, or 9 stationary points corresponding to attractive or repulsive centers (1--5) and saddle points (0--4). A physical analysis of the model is performed.

gr-qc↗
arXiv2019

Qualitative and Numerical Analysis of a Cosmological Model Based on an Asymmetric Scalar Doublet with Minimal Couplings. II. Numerical Modeling of Phase Trajectories

With the help of our own software package DifEqTools, numerical modeling of the cosmological evolution of a system consisting of an asymmetric scalar doublet of nonlinear, minimally interacting scalar fields, a classical field and a phantom field, has been performed. Peculiarities of the behavior of the model near zeroenergy hypersurfaces have been revealed.

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arXiv2019

Qualitative and Numerical Analysis of a Cosmological Model Based on an Asymmetric Scalar Doublet with Minimal connections. III. Multiply-connected Factor and Character of the Singular Points

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, both classical and phantom, the behavior of the model near zero energy hypersurfaces has been revealed. The influence of the multiply connected factor of the phase space of the dynamical system, this factor being a consequence of the nonanalyticity of the coefficients of an autonomous system of differential equations, is discussed. The character of all singular points is revealed.

gr-qc↗
arXiv2019

On Euclidean limit cycles in cosmological models based on scalar fields

A detailed analysis of the phase trajectories of cosmological models based on classical and scalar fields near surfaces of zero effective energy has been carried out. A study of the differential parameters of the convergence of phase trajectories to a zero-energy surface boundary shows that the phase trajectories merge within a finite time with the phase trajectories of free oscillations corresponding to zero effective energy. This confirms the assumption formulated in a number of previous works by one of the authors about the existence of Euclidean limit cycles in cosmological models based on scalar fields with a Higgs interaction potential.

gr-qc↗
arXiv2019

Dynamics of cosmological models with nonlinear classical phantom scalar fields. II. Qualitative analysis and numerical modeling

A detailed qualitative analysis and numerical modeling of the evolution of cosmological models based on nonlinear classical and phantom scalar fields with self-action are performed. Complete phase portraits of the corresponding dynamical systems and their projections onto the Poincaré sphere are constructed. It is shown that the phase trajectories of the corresponding dynamical systems can, depending on the parameters of the model of the scalar field, split into bifurcation trajectories along 2, 4, or 6 different dynamical flows. In the phase space of such systems, regions can appear which are inaccessible for motion. Here phase trajectories of the phantom scalar field wind around one of the symmetric foci (centers) while the phase trajectories of the classical scalar field can have a limit cycle determined by the zero effective energy corresponding to a Euclidean Universe.

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arXiv2019

Dynamics of cosmological models with nonlinear classical phantom scalar fields. I. Formulation of the mathematical model

Mathematical models describing the cosmological evolution of classical and phantom scalar fields with self-action are formulated and analyzed. Systems of dynamical equations in the plane, describing homogeneous cosmological models, have been obtained. It is shown that depending on the parameters of the field model, it is possible to violate the singly-connectedness of the phase space of the corresponding dynamical model.

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arXiv2017

A qualitative and numerical analysis of cosmological models based on assymetric scalar doublet: classical + phantom scalar field. I. A case of minimally interacting scalar fields: the qualitative analysis

The paper provides a qualitative and numerical analysis-based investigation of cosmological models founded on an asymmetrical scalar doublet comprising of a classical and a phantom scalar fields. Presence of a phantom scalar field allows one to consider also classical scalar fields with attraction of like-charged particles which significantly extends a diversity of cosmological models' behaviours. It is shown that a cosmological model based on an asymmetric scalar doublet in the case of minimal interaction has 9 singular points 2 of which are attractive and the rest are non-stable saddle ones. It is also shown that a presence of even essentially weak phantom field significantly changes the dynamics of a cosmological model.

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arXiv2017

A macroscopic view to the standard cosmological model

The averaging of the dynamic functions of the standard cosmological model (SCM) at its early stage with the dominance of the scalar field is carried out. It is shown that microscopic oscillations with Compton period provide the major contribution to the macroscopic energy density of the scalar field at large times at this stage. In this case, the effective equation of state of the scalar field oscillates between the inflationary and the extremely rigid ones, while the macroscopic equation of state is non-relativistic.

gr-qc↗
arXiv2016

The Qualitative and Numerical Analysis of the Cosmological Model Based on Phantom Scalar Field with Self

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. {\bf keywords}: cosmological model, phantom scalar field, quality analysis, asymptotic behavior, numerical simulation, numerical gravitation.\\ {\bf PACS}: 04.20.Cv, 98.80.Cq, 96.50.S 52.27.Ny

gr-qc↗
arXiv2015

Collisionless self-gravitating statistical systems of scalar interacting particles

This paper is devoted to consideration of the theory of collisionless statistical systems with interparticle scalar interaction. The mathematical model of such systems is constructed and the exact solution of Vlasov equation for isotropic homogenous model of the Universe is found. Asymptotic solutions of self-consistent Vlasov - Einstein model for conformally invariant scalar interactions are found.

gr-qc↗
arXiv2015

Nonminimal Macroscopic Models of a Scalar Field Based on Microscopic Dynamics. II. Transport Equations

The article proposes generalizations of the macroscopic model of plasma of scalar charged particles to the cases of inter-particle interaction with multiple scalar fields and negative effective masses of these particles. The model is based on the microscopic dynamics of a particle at presence of scalar fields. The theory is managed to be generalized naturally having strictly reviewed a series of its key positions depending on a sign of particle masses. Thereby, it is possible to remove the artificial restriction contradicting the more fundamental principle of action functional additivity. Additionally, as a condition of internal consistency of the theory, particle effective mass function is found.

gr-qc↗
arXiv2015

Nonminimal Macroscopic Models of a Scalar Field Based on Microscopic Dynamics. I. Extension of the Theory for Negative Masses

The article proposes generalizations of the macroscopic model of plasma of scalar charged particles to the cases of inter-particle interaction with multiple scalar fields and negative effective masses of these particles. The model is based on the microscopic dynamics of a particle at presence of scalar fields. The theory is managed to be generalized naturally having strictly reviewed a series of its key positions depending on the sign of particle masses. Thereby, it is possible to remove the artiicial restriction contradicting the more fundamental principle of action functional additivity.

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arXiv2013

Cosmological evolution of the cosmological plasma with interpartial scalar interaction. II. Formulation of mathematical model

On the basis of the relativistic kinetic theory the relativistic statistical systems with scalar interaction particles are investigated. The self-consistent system of the equations describing self-gravitating plasma with interpartial scalar interaction is formulated, macroscopical laws of preservation are received. The closed system of the equations describing cosmological models to which the matter is presented by plasma with interpartial scalar interaction is received.

gr-qc↗
arXiv2013

Cosmological evolution of the cosmological plasma with interpartial scalar interaction. III. Model with the attraction of the like scalar charged particles

On the basis of the relativistic kinetic theory the mathematical model of cosmological plasmas with an attraction of the like charged scalar particles is formulated. It is shown, that cosmological the model, based on a classical scalar field with an attraction, is unsatisfactory, that leads to necessity of attraction of phantom models of a scalar field for systems with an attraction.

gr-qc↗
arXiv2013

The cosmological evolution of the cosmological plasma with interpartial scalar interaction. I. The canonic formulation of classical scalar interaction

On the basis of Hamilton a formalism the dynamic equations of movement scalar charged particles in a classical scalar field are formulated. Unlike earlier published works of the author the model with zero own weight of particles is considered. Linear integrals of movement are found and ambiguity of communication between kinematic speed and an impulse of particles is specified.

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