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

A mathematical model of the evolution of spherical perturbations in an ideal cosmological scalar-charged fluid coupled to the Higgs field is constructed. A closed mathematical model of linear spherical perturbations in a cosmological medium of a scalar-charged ideal fluid with scalar Higgs interaction is formulated. It is shown that spherical perturbations of the Friedmann metric are possible only in the presence of an isotropic fluid. At singular points of the background cosmological model, perturbations of the metric do not occur and perturbations are described by a vacuum-field model. Exact solutions are obtained at singular points of the cosmological system; the scalar field perturbations are shown to be traveling waves in the case of a stable singular point of the cosmological system and exponentially growing standing waves in the case of an unstable singular point. Using numerical modeling, the formation of a stratified halo in the form of growing standing waves is shown.