Quantum gravity, dynamical triangulations and higher derivative regularization

We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the EinsteinHilbert action plus an R-term. The phase diagram as a function of the bare coupling constants is studied in the search for a sensible continuum limit. For small values of the coupling constant of the R term the model seems to belong to the same universality class as the model with pure Einstein-Hilbert action and exhibits the same phase transition. The order of the transition may be second or higher. The average curvature is positive at the phase transition, which makes it difficult to understand the possible scaling relations of the model. Partly supported by the KBN grant no. 2 0053 91 01