Abstract
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 at early stages of expansion arises in the model under study at sufficiently large scalar charges, and the instability develops near unstable points of the vacuum doublet. Short-wave 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).
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