Cosmological models based on a statistical system of scalar charged degenerate fermions and an asymmetric Higgs scalar doublet

Abstract

Abstract: 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 an Hamiltonian formalisms, a function of the dynamical mass of scalar-charged particles is constructed and it is shown that the nonnegativity condition for this function has to be removed for the consistency of the theory. 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. The full correspondence of these equations to microscopic equations with singular sources is demonstrated. On the basis of the obtained equations, a cosmological model for a degenerate system of scalar-charged fermions is formulated. An exact solution of the constitutive equations for a degenerate scalar-charged plasma in the cosmological model is obtained, which allows significantly simplifying 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 single-scalar-charged fermions and the other has one kind of fermions charged with two charges of various nature. A qualitative analysis of the obtained 6-dimensional dynamical system for a two-component model is carried out. It is shown that in such models, acceleration deceleration modes become possible at the late stages of the evolution of the Universe.