Massive fields temper anomaly-induced inflation: the clue to graceful exit?

A method of calculating the vacuum effective action for massive quantum fields in curved spacetime is outlined. Our approach is based on the conformal representation of the fields action and on the integration of the corresponding conformal anomaly. As a relevant cosmological application, we find that if taking the masses of the fields into account, then the anomaly-induced inflation automatically slows down. The only relevant massive fields for this purpose turn out to be the fermion fields. So in supersymmetric theories this mechanism can be specially efficient, for it may naturally provide the graceful exit from the inflationary to the FLRW phase. Taking the SUSY breaking into account, the anomaly-induced inflation could be free of the well-known difficulties with the initial data and also with the amplitude of the gravitational waves.