Complete model of cosmological evolution of a classical scalar field with the Higgs potential. I. Analysis of the model

TL;DR

This paper develops and analyzes a comprehensive cosmological model involving a classical scalar field with the Higgs potential, exploring its dynamics without assuming a nonnegative Hubble constant, and classifies the topology of the associated Einstein-Higgs hypersurfaces.

Contribution

It provides a complete analysis and simulation of the cosmological evolution of a scalar field with Higgs potential, including a classification of the global phase space topology.

Findings

Classified the topology of Einstein-Higgs hypersurfaces.

Performed computer simulations without assuming nonnegative Hubble constant.

Analyzed the global properties of phase trajectories in the model.

Abstract

A complete model of cosmological evolution of a classical scalar field with the Higgs potential is studied and simulated on a computer without assumption that the Hubble constant is nonnegative. The corresponding dynamical system is qualitatively analyzed and the Einstein-Higgs hypersurfaces the topology of which determines the global properties of the phase trajectories of the cosmological model are classified.