Some notes on the Weyl geometry, particle production and induced gravity

A short introduction to Weyl geometry and Weyl gravity is given. The self-consistency relation for the variation of the general form of the matter action integral to be conformal invariant is obtained. It is shown that the particle production rate per unit coordinate volume per unit coordinate time is conformal invariant. It is noticed that such a feature allows us to consider the perfect fluid action as an example of the Sakharov’s induced gravity model.