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Based on the previously formulated mathematical model of a statistical systemwith scalar interaction of fermions and the theory of gravitational-scalarinstability of a cosmological model based on a two-component statistical systemof scalar-charged degenerate fermions, a numerical model of the cosmologicalevolution of gravitational-scalar perturbations is constructed and specificexamples of the development of instability are given. Some features of theinstability's development are investigated depending on the nature of thebehavior of the unperturbed cosmological model. It is shown that unstable modescan appear at very early stages of cosmological expansion or contraction, andthe duration of the unstable phase is comparable to tens of Planck scales. Inthis case, however, a very significant increase in unstable modes is possibledue to the redistribution of energy between the components of the scalardoublet.

Gravitational - Scalar Instability of a Two-Component Degenerate System of Scalar Charged Fermions with Asymmetric Higgs Interaction