Abstract
A mathematical model of the evolution of plane perturbations in the cosmological statistical system of completely degenerate scalar-charged fermions with Higgs scalar interaction for short-wave perturbations is formulated. These disturbance modes have been found and investigated. It is shown that in such a model an additional oscillation mode arises, which is associated directly with degenerate fermions, in which monotonically decreasing and increasing perturbations of the metric exist. In this case, there is such a time instant in the system that the potential of the scalar field, together with the energy density, tends to infinity. In this regard, an assumption is made about a possible mechanism for the formation of dark matter condensates.
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