  We argue that 4D gravity is drastically modified at distances larger than the
horizon scale, due to the large infrared quantum fluctuations of the conformal
part of the metric. The infrared dynamics of the conformal factor is generated
by an effective action, induced by the trace anomaly of matter in curved space,
analogous to the Polyakov action in two dimensions. The resulting effective
scalar theory is renormalizable, and possesses a non-trivial, infrared stable
fixed point, characterized by an anomalous scaling dimension of the conformal
factor. We argue that this theory describes a large distance scale invariant
phase of 4D gravity and provides a framework for a dynamical solution of the
cosmological constant problem.
