Cosmological models based on an asymmetric scalar doublet with kinetic coupling of components. I. General properties of the cosmological model

TL;DR

This paper develops and analyzes a cosmological model based on an asymmetric scalar doublet with kinetic coupling, exploring its properties, symmetry, and behavior near singularities through qualitative and numerical methods.

Contribution

It introduces a novel cosmological model with kinetic coupling between classical and phantom scalar fields and provides a detailed qualitative and numerical analysis of its properties.

Findings

Model exhibits symmetry and invariance properties.

Near singularities, the universe behaves like an ideal fluid with a rapid equation of state.

Numerical simulations illustrate the evolution for specific parameters.

Abstract

A mathematical model of the Universe evolution, based on asymmetric doublet of classical and phantom dcalar Higgs fields with a kinetic connection between the components, has been constructed and studied. A detailed qualitative analysis was carried out, the properties of the model's symmetry and invarience with respect to the similariry transformations of fundamental constants were proven. The principles of numerical modeling are formulated and an example of numerical modeling of the evolution of the model for a specific set of fundamental constants and initial conditions is given. the asymptotic behavior of the model near cosmological singularities is studied. It is shown that cosmological model near singularities manifests itself as an ideal fluid with an extremelly ripid equation of state. Keywords: cosmological model, phantom and classical scalar fields, kinetic interection, quality analysis, asymptotic behavior, numerrical modeling.