  Based on the previously formulated mathematical model of a statistical system
with scalar interaction of fermions and the theory of gravitational-scalar
instability of a cosmological model based on a two-component statistical system
of scalar-charged degenerate fermions, a numerical model of the cosmological
evolution of gravitational-scalar perturbations is constructed and specific
examples of the development of instability are given. Some features of the
instability's development are investigated depending on the nature of the
behavior of the unperturbed cosmological model. It is shown that unstable modes
can appear at very early stages of cosmological expansion or contraction, and
the duration of the unstable phase is comparable to tens of Planck scales. In
this case, however, a very significant increase in unstable modes is possible
due to the redistribution of energy between the components of the scalar
doublet.

General Relativity and Quantum Cosmology