Dynamics of the conformal factor in 4D gravity
  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. 
I. Antoniadis