On the phenomenological description of particle creation and its   influence on the space-time metrics
  The method is proposed for the phenomenological description of particle creation by external fields (in the presence of gravitational field or without it). It is shown that, despite the appearance of the non-dynamical degrees of freedom, such as the number density and four-velocities of particles at the moment of creation (and corresponding Lagrange multipliers) the theory is complete and self-consistent. It appears that the very existence of particle creation processes requires the non-zero trace anomaly of the external quantum field under consideration. 
Victor Berezin
gr-qc