Litim and Satz have just addressed a question I've long wondered about. http://arxiv.org/abs/1205.4218 Limit cycles and quantum gravity Daniel Litim, Alejandro Satz We study renormalization group equations of quantum gravity in four dimensions. We find an ultraviolet fixed point in accordance with the asymptotic safety conjecture, and infrared fixed points corresponding to general relativity with positive, vanishing or negative cosmological constant. In a minisuperspace approximation, we additionally find a renormalization group limit cycle shielding the ultraviolet from the infrared fixed points. We discuss implications of this pattern for asymptotically safe gravity in the continuum and on the lattice. They have an interesting bit of speculation at the end: "Finally we mention that a degenerate limit cycle oers a new scenario for asymptotic safety in that no ne-tuning of UV initial conditions is required. Instead, all trajectories enter an extended semiclassical regime and lead to a tiny positive cosmological constant in the infrared."