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

Abstract

A 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 transition rules between them are constructed. We qualitatively analyze the obtained dynamical systems and model them numerically. A mathematical model of plane longitudinal scalar–gravitational perturbations of the Friedmann ideal charged fluid with Higgs interaction is formulated. It is shown that gravitational perturbations do not arise in the absence of the fluid, i.e., in the vacuum-field model. Perturbations of the scalar field are possible only in those cases where the cosmological system is at singular points in the unperturbed state. In these cases, exact solutions of the field equation are found in terms of Bessel functions of the first and second kind; they describe 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 the general form and are solved for a neutral fluid. 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 1985 model of Khlopov, Malomed, and Zeldovich. 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.