SCALING BEHAVIOR OF QUANTUM 4-GEOMETRIES

We propose that large quantum fluctuations of the conformal factor dra stically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive scaling relations for the partition function and physical observables in this conformal phase, and suggest quantita tive tests of these relations in numerical simulations of simplicial f our geometries with S4 topology. In particular, we predict the form of the critical curve in the coupling constant plane, and determine the scaling of the Newtonian coupling with volume which permits a sensible continuum limit. The existing numerical results already provide some evidence of this infrared fixed point and new conformal invariant phas e of quantum gravity.