Complete cosmological model based on a asymmetric scalar Higgs doublet

TL;DR

This paper develops a comprehensive cosmological model using an asymmetric scalar Higgs doublet, analyzing its dynamics without assuming nonnegative universe expansion, and explores the model's global properties through qualitative and numerical methods.

Contribution

It introduces a complete dynamical system for a cosmological model with classical and phantom Higgs fields, removing previous assumptions about expansion rate positivity.

Findings

Different topologies of the Einstein-Higgs hypersurface are identified.

Various asymptotic behaviors of the universe are classified.

Numerical simulations illustrate diverse cosmological evolutions.

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.