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A mathematical model of the evolution of plane perturbations in thecosmological statistical system of completely degenerate scalar-chargedfermions with Higgs scalar interaction for short-wave perturbations isformulated. These disturbance modes have been found and investigated. It isshown that in such a model an additional oscillation mode arises, which isassociated directly with degenerate fermions, in which monotonically decreasingand increasing perturbations of the metric exist. In this case, there is such atime instant in the system that the potential of the scalar field, togetherwith the energy density, tends to infinity. In this regard, an assumption ismade about a possible mechanism for the formation of dark matter condensates.

gravitation and cosmology/gravitation and cosmology

The Stability of the Cosmological System of Degenerate Scalar Charged  Fermions and Higgs Scalar Fields. II. The Evolution of Short-Wave  Perturbations