  A method of calculating the vacuum effective action for massive quantum
fields in curved space-time 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.
