Complete cosmological model based on a asymmetric scalar Higgs doublet

Abstract

A study of a complete cosmological model based on an asymmetric scalar doublet represented by the classical and phantom scalar Higgs fields is carried out. At the same time, the assumption about the nonnegativity of the expansion rate of the Universe, which in some cases contradicts the complete system of Einstein's equations, was removed. A closed system of dynamic equations describing the evolution of the cosmological model is formulated, and the dependence of the topology of the Einstein -Higgs hypersurface of the 5-dimensional phase space of the dynamical system that determines the global properties of the cosmological model on the fundamental constants of the model is investigated. A qualitative analysis of the dynamical system of the corresponding cosmological model is carried out, asymptotic phase trajectories are constructed, and the results of numerical modeling are presented, illustrating various types of behavior of the cosmological model.

Single-Field Model of Gravitational-Scalar Instability. II. Black Hole Formation

“…In addition, we write down the expression we need below for densities of scalar charges, ρ (a) , which are determined using the charge number density n (a) [12] and not coincide in general with the scalar charge densities σ z and σ ζ introduced above:…”

“…In what follows, we will need the coordinates of singular points of the vacuum scalar Higgs doublet of the background metric in the 3-dimensional subspace R 3 {H, Φ, ϕ} of the 5-dimensional phase space of the corresponding dynamical system R 5 = {H, Φ, Z, ϕ, z} [12], since these points largely determine the dynamics of the M 1 background model. 5 For positive fundamental parameters α, β, Λ , there are 18 such singular points.…”

“…In what follows, we will need the coordinates of stable (attractive) singular points of the dynamical system of the unperturbed cosmological model with vacuum asymmetric scalar Higgs doublet in the threedimensional phase subspace of the phase space of the corresponding 5-dimensional dynamical system R 3 : [Φ, ϕ, H, Z = 0, z = 0] 7 . According to [12], there are only 2 such symmetrical stable equilibrium points:…”

Gravitational-Scalar Instability of a Two-Component Degenerate System of Scalarly Charged Fermions with Asymmetric Higgs Interaction

“…Note that in vacuum the one-dimensional dynamical system with Φ = Φ(x) corresponding to the equation ( 14) has two singular points (see, for example, [7])…”

“…Let's turn to the equations of motion (7). Instead of directly solving these equations, let's turn to their integrals of motion, which have the form [5]:…”