  Solutions of the system of evolutionary equations in the short-wavelength
approximation are found and studied. A connection is established between the
problem of the evolution of short-wavelength gravitational-scalar perturbations
and the problem of eigenvectors and eigenvalues of a linear operator. By means
of an applied mathematical package, a program for calculating the amplitudes of
perturbations of the cosmological model was created. It is shown that unstable
short-wavelength perturbation modes arise in such a system. A numerical model
for the evolution of gravitational-scalar perturbations of the cosmological
model has been constructed and analyzed.
