  Starting with the idea to describe phenomenologically the particle creation
in the strong gravitational fields, we introduced explicitly the particle
number nonconservation (= creation law) into the action integral with the
corresponding Lagrange multiplier. Following the fundamental result by Ya. B.
Zel'dovich and A. A. Starobinsky (1977) we then postulated that the rate of
particle creation is proportional to the square of Weyl tensor. Concerning the
conformal invariance, yet another question arises: how the scalar field could
know about the surgery made on the metric tensor (if such an invariance is the
fundamental law of Nature and not just the mathematical exercise)? The only way
is that the scalar field is itself the part of metric, namely, the conformal
factor. We showed, that such an identification results in the natural
appearance of the quartic self-interaction term in the scalar field Lagrangian,
which is needed to make particle massive. And it is just quartic, because our
space-time is four-dimensional.
