A Theory for the Conformal Factor in Quantum $R^2$ Gravity
  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. 
E. Elizalde and S.D. Odintsov