  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.
