  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 scalarly charged degenerate fermions, a numerical model of the cosmological
evolution of gravitational-scalar perturbations in the presence of classical
and phantom scalar fields is constructed and studied. The gravitational-scalar
instability in the early stages of expansion in the model under study arises at
sufficiently large scalar charges, and the instability develops near the
unstable points of the vacuum doublet. Shortwave perturbations of the free
phantom field turn out to be stable at stable singular points of the vacuum
doublet. It is shown that for sufficiently large scalar charges, mass
perturbations can grow to the values of masses Black Hole Seeds (BHS).
