A Complete Model of Cosmological Evolution of a Scalar Field with Higgs Potential and Euclidean Cycles

Complete cosmological model based on a asymmetric scalar Higgs doublet

“…Statement 2. The function h(τ ) minimum and maximum points lie on the surface of the effective potential (49), and the singular points of the dynamical system are the extremum points of this surface (see Fig. 2).…”

“…Thus, in the general case, a dynamic system can have 18 singular points 7 . These singular points are located at the intersection of the perpendiculars to the 9 points of the base rectangle with the surface of the effective potential (49). These are, firstly, two symmetric points located on the Oh -…”

“…More precisely, the restriction of the Hubble constant to non-negative values (1) may contradict the original system of Einstein's equations. This useful discussion resulted in the article [49], in which it was shown that the condition (1) for H → 0 actually contradicts the original system of Einstein-Higgs equations in the case of the classical Higgs field. Based on the formulated complete system of Einstein -Higgs equations 3 In [49], a qualitative and numerical-analytical study of the original the system of dynamical equations for the classical Higgs field, and the possibility in a number of cases of changing the expansion phase to the compression phase in the corresponding cosmological model is shown.…”

“…In the course of this research, we will, first, widely use the concept of Einstein-Higgs hypersurface introduced in [49], the topology of which determines the global behavior of the dynamical system. Second, we will apply the methods of the qualitative theory of dynamical systems (see, for example, [36]) to determine the asymptotic behavior of the cosmological model for arbitrary values of the parameters of the field model.…”

Cosmological Evolution of a Statistical System of Degenerate Scalarly Charged Fermions with an Asymmetric Scalar Doublet. I. Two-Component System of Assorted Charges

“…In [8], a qualitative and numerical analysis of quintom models was carried out under the assumption of nonnegativity of the Hubble parameter (H 0). However, it was shown in [9] that this assumption * E-mail: ignatev-yurii@mail.ru may contradict the complete set of Einstein equations and the scalar field at H → 0. In the same paper, the concept of an Einstein-Higgs hypersurface was introduced, the topology of which largely determines the global properties of cosmological models based on an asymmetric scalar doublet.…”