  When quantizing Conformal Dilaton Gravity there is a conformal anomaly which
starts at two loop order. This anomaly stems from evanescent operators on the
divergent parts of the effective action. The general form of the finite
counterterm which is necessary in order to insure cancellation of the Weyl
anomaly to every order in perturbation theory has been determined using only
conformal invariance . Those finite counterterms do not have any inverse power
of any mass scale in front of them (precisely because of conformal invariance)
and then they are not negligible in the low energy deep infrared limit. The
general form of the ensuing modifications to the scalar field equation of
motion has been determined and some physical consequences extracted.
