Evolution of plane perturbations in the cosmological environment of the Higgs scalar field and an ideal scalar charged fluid

TL;DR

This paper develops a mathematical and numerical framework to analyze plane scalar gravitational perturbations in a cosmological model involving Higgs scalar fields and an ideal scalar charged fluid, revealing conditions for stability and instability.

Contribution

It introduces a new phenomenological model of an ideal fluid with scalar charge and analyzes scalar perturbations within this framework, including exact solutions and WKB approximation results.

Findings

Perturbations do not arise in the vacuum-field model.

Exact solutions show damped or growing oscillations depending on stability.

Instability occurs only during the unstable inflationary phase.

Abstract

A phenomenological model of an ideal fluid with a scalar charge is formulated, on the basis of which a model with a neutral fluid and a vacuum-field model with rules of transition between them are constructed. A qualitative analysis of the obtained dynamic systems is carried out and numerical cosmological models based on these systems are constructed. A mathematical model of plane longitudinal scalar-gravitational perturbations of the Friedmann ideal charged fluid with Higgs interaction is formulated. It is shown that in the absence of fluid, i.e., in the vacuum-field model, gravitational perturbations do not arise. Perturbations of the scalar field are possible only in those cases when in the unperturbed state the cosmological system is at singular points. For these cases, exact solutions of the field equation are found, expressed in Bessel functions of the first and second kind and describing damped oscillations in the case of a stable unperturbed state and growing oscillations in the case of an unstable unperturbed state. The WKB theory of plane scalar-gravitational perturbations is constructed: dispersion equations are obtained in general form and solved for a neutral fluid. In this case, expressions are obtained for the local frequency and growth increment of oscillations, as well as the integral increment. It is shown that only free wave regimes or growing standing oscillations are possible during the evolution. Perturbations in the WKB approximation in a neutral fluid are studied and it is shown that local formulas for the evolution of perturbations correspond to the model of the 1985 article by M.Yu. The times of the beginning and end of the instability phase are determined and it is shown that instability can develop only at the unstable inflationary stage of the expansion of the Universe.