Cosmological Models Based on an Asymmetric Scalar Doublet with Kinetic Coupling of Components. I. General Properties of the Cosmological Model

A mathematical model of the evolution of the Universe, based on an asymmetric doublet of classical and phantom scalar Higgs fields with a kinetic connection between the components, is constructed and studied. A detailed qualitative analysis is carried out, the properties of the modelCs symmetry and invariance with respect to the similarity transformation of fundamental constants are proven. The principles of numerical modeling are formulated, and an example of numerical modeling of the model evolution is given for a specific set of fundamental constants and initial conditions. The asymptotic behavior of the model near cosmological singularities is studied, and It is shown that it then manifests itself as a perfect fluid with an extremely rigid equation of state.