  The conformal anomaly induced sector of four-dimensional quantum gravity
(infrared quantum gravity) ---which has been introduced by Antoniadis and
Mottola--- is here studied on a curved fiducial background. The one-loop
effective potential for the effective conformal factor theory is calculated
with accuracy, including terms linear in the curvature. It is proven that a
curvature induced phase transition can actually take place. An estimation of
the critical curvature for different choices of the parameters of the theory is
given.
