  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.
