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 Poincar\'e 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.Comment: 10 pages, 16 figure

Numerical Models of Cosmological Evolution of the Degenerated Fermi-system of Scalar Charged Particles

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.Comment: 15 pages, 14 figures, 4 reference

Qualitative and numerical analysis of a cosmological model based on a phantom scalar field with self-interaction

© 2017, Pleiades Publishing, Ltd. We investigate the asymptotic behavior of a cosmological model based on a phantom scalar field by qualitative analysis of the set of differential equations. We show that, as opposed to models with a classical scalar field, such models have stable asymptotic solutions with a constant value of the potential both in the infinite past and the infinite future. We also develop numerical models of the cosmological evolution with a phantom scalar field

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

© 2015, Pleiades Publishing, Ltd. Based on the previously constructed mathematical model of a statistical Fermi system with particle interaction, in this paper we construct and analyze numerical models of cosmological evolution of a single-component degenerate Fermi system of scalar particles. The applied mathematics package Mathematica 9 is used for numerical model construction. It is strictly proved that the conservation law for the total energy of the scalarly charged degenerate Fermi system and a massive scalar field is a differential consequence of the particle number conservation law. Thus the mathematical model of cosmological evolution of the system is reduced to a closed normal set of three essentially nonlinear ordinary differential equations. After transforming the equations to dimensionless variables, an algorithm of its numerical solution is suggested. On the basis of numerical simulation of the cosmological evolution we show the presence of a new phenomenon in the cosmological evolution: it is the phenomenon of phantom bursts of cosmological acceleration at times of the order of 103 Planck times

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

© 2015, Pleiades Publishing, Ltd. Based on the previously constructed mathematical model of a statistical Fermi system with particle interaction, in this paper we construct and analyze numerical models of cosmological evolution of a single-component degenerate Fermi system of scalar particles. The applied mathematics package Mathematica 9 is used for numerical model construction. It is strictly proved that the conservation law for the total energy of the scalarly charged degenerate Fermi system and a massive scalar field is a differential consequence of the particle number conservation law. Thus the mathematical model of cosmological evolution of the system is reduced to a closed normal set of three essentially nonlinear ordinary differential equations. After transforming the equations to dimensionless variables, an algorithm of its numerical solution is suggested. On the basis of numerical simulation of the cosmological evolution we show the presence of a new phenomenon in the cosmological evolution: it is the phenomenon of phantom bursts of cosmological acceleration at times of the order of 103 Planck times

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

© 2014, Pleiades Publishing, Ltd. Based on the authors’ approach to the macroscopic description of scalar interactions, this paper develops a macroscopic model of a relativistic plasma with phantom scalar interaction of elementary particles. In this paper, macroscopic equations for a statistical system with scalar interaction of particles are obtained, and a complete set of macroscopic equations describing cosmological models is built

Cosmological evolution of statistical system of scalar charged particles

© 2015, Springer Science+Business Media Dordrecht. In the paper we consider the macroscopic model of plasma of scalar charged particles, obtained by means of the statistical averaging of the microscopic equations of particle dynamics in a scalar field. On the basis of kinetic equations, obtained from averaging, and their strict integral consequences, a self-consistent set of equations is formulated which describes the self-gravitating plasma of scalar charged particles. It was obtained the corresponding closed cosmological model which also was numerically simulated for the case of one-component degenerated Fermi gas and two-component Boltzmann system. It was shown that results depend weakly on the choice of a statistical model. Two specific features of cosmological evolution of a statistical system of scalar charged particles were obtained with respect to cosmological evolution of the minimal interaction models: appearance of giant bursts of invariant cosmological acceleration Ω at the time interval 8⋅103–2⋅104 tPl and strong heating (3–8 orders of magnitude) of a statistical system at the same times. The presence of such features can modify the quantum theory of generation of cosmological gravitational perturbations