Toward Understanding the Conformal Gravity

Abstract

We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the usual hydrodynamic 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 dilaton gravity action integral. Thus, we obtained something like the induced gravity suggested first by A. D. Sakharov. It is shown that the resulting system is self-consistent.