  We constructed the conformally invariant model for scalar particle creation
induced by strong gravitational fields. Starting from the "usual"
hydrodynamical description of the particle motion written in the Eulerian
coordinates we substituted the particle number conservation law (which enters
the formalism) by "the particle creation law", proportional to the square of
the Weyl tensor (following the famous result by Ya.B.Zel`dovich and A.
A.Starobinsky). Then, demanding the conformal invariance of the whole dynamical
system, we have got both the (Weyl)-conformal gravity and the Einstein--Hilbert
gravity action integral with dilaton field. Thus, we obtained something like
the induced gravity suggested first by A. D.Sakharov. It is shown that the
resulting system is self-consistent. We considered also the vacuum equations.
It is shown that, beside the "empty vacuum", there may exist the "dynamical
vacuum", which is nothing more but the Dirac sea.
