Conformal invariance and phenomenology of particle creation: Weyl geometry vs. Riemannian geometry

Using the example of an action for an ideal fluid with a variable number of particles, we study a phenomenological description of the processes of particle production in the background of strong external fields, including gravity and scalar fields. This model is discussed for Weyl geometry and Riemannian geometry. A new invariant related to the interaction of the Weyl vector with particles is incorporated into the considered matter action. The conformal invariance of the term in the matter action responsible for the particle production is demonstrated.