  A new theory for the conformal factor in R$^2$-gravity is developed. The
infrared phase of this theory, which follows from the one-loop renormalization
group equations for the whole quantum R$^2$-gravity theory is described. The
one-loop effective potential for the conformal factor is found explicitly and a
mechanism for inducing Einstein gravity at the minimum of the effective
potential for the conformal factor is suggested. A comparison with the
effective theory of the conformal factor induced by the conformal anomaly, and
also aiming to describe quantum gravity at large distances, is done.
