  In the paper we consider the macroscopic model of plasma of scalar charged
particles, obtained by means of the statistical averaging of the microscopic
equations of particle dynamics in a scalar field. On the basis of kinetic
equations, obtained from averaging, and their strict integral consequences, a
self-consistent set of equations is formulated which describes the
self-gravitating plasma of scalar charged particles. It was obtained the
corresponding closed cosmological model which also was numerically simulated
for the case of one-component degenerated Fermi gas and two-component Boltzmann
system. It was shown that results depend weakly on the choice of a statistical
model. Two specific features of cosmological evolution of a statistical system
of scalar charged particles were obtained with respect to cosmological
evolution of the minimal interaction models: appearance of giant bursts of
invariant cosmological acceleration $\Omega$ at the time interval
$8\cdot10^3\div2\cdot10^4 t_{Pl}$ and strong heating ($3\div 8$ orders of
magnitude) of a statistical system at the same times. The presence of such
features can modify the quantum theory of generation of cosmological
gravitational perturbations.
