Dynamics of cosmological models with nonlinear classical phantom scalar fields. I. Formulation of the mathematical model

TL;DR

This paper formulates and analyzes mathematical models of cosmological evolution involving classical and phantom scalar fields, revealing how parameter choices can affect the phase space structure of these models.

Contribution

It introduces a new formulation of dynamical equations for homogeneous cosmological models with scalar fields, highlighting phase space properties.

Findings

Phase space can become multiply connected depending on model parameters.

Dynamical equations are derived for homogeneous cosmological models.

The model allows for analysis of scalar field effects on cosmological evolution.

Abstract

Mathematical models describing the cosmological evolution of classical and phantom scalar fields with self-action are formulated and analyzed. Systems of dynamical equations in the plane, describing homogeneous cosmological models, have been obtained. It is shown that depending on the parameters of the field model, it is possible to violate the singly-connectedness of the phase space of the corresponding dynamical model.