Complete cosmological model based on an asymmetric scalar Higgs doublet

We study a complete cosmological model based on an asymmetric scalar doublet represented by the classical and phantom scalar Higgs fields. Moreover, we remove the assumption that the expansion rate of the Universe is nonnegative, which contradicts the complete system of Einstein's equations in several cases. We formulate a closed system of dynamical equations describing the evolution of the cosmological model and study the dependence of the topology of the Einstein-Higgs hypersurface of the five-dimensional phase space of the dynamical system that determines the global properties of the cosmological model based on the fundamental constants of the model. We analyze the dynamical system of the corresponding cosmological model qualitatively, construct asymptotic phase trajectories, and present numerical modeling results illustrating various types of behavior of the cosmological model.