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On the basis of the general relativistic statistical and kinetic theory, aconsistent closed cosmological model is formulated. It is based on astatistical system of scalar charged fermions interacting by means of classicaland phantom scalar fields. Based on the study of the microscopic dynamics ofscalar charged particles, within the framework of the Lagrangian as well asHamiltonian formalism, a function of the dynamic mass of scalar chargedparticles was constructed and it was shown that for the consistency of thetheory, it is necessary to remove the nonnegativity condition for thisfunction. On the basis of the Lagrangian formalism, equations of gravitationaland scalar fields with singular sources are formulated and microscopicconservation laws are obtained. Within the framework of the generalrelativistic kinetic theory, macroscopic equations of gravitational and scalarfields are formulated and macroscopic conservation laws are obtained. Theseequations' full correspondence to microscopic equations with singular sourcesis shown. Further, on the basis of the obtained equations, a cosmological modelfor a degenerate system of scalarly charged fermions is formulated. An exactsolution of the constitutive equations for a degenerate scalar-charged plasmain the cosmological model is obtained, which made it possible to significantlysimplify the original system of equations. On the basis of the obtainedsolution of the constitutive equations, two fundamentally differentcosmological models are formulated, one of which has two types of singlyscalarly charged fermions, while the second has one kind of fermions chargedwith two charges of various nature. A qualitative analysis of the obtained6-dimensional dynamic system for a two-component model is carried out.

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