Based on one the authors' approach to a macroscopic description of the scalar interaction, we develop a macroscopic model of a relativistic plasma with a phantom scalar interaction of elementary particles. In this model, as opposed to previous models, the restriction of nonnegativity of the particles' effective mass is removed.

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.

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 artificial restriction contradicting the more fundamental principle of action functional additivity.

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.