Selecting a scale, the conformal convergence problem and R2 terms

The Einstein-Hilbert action contains negative norm terms such as the conformal factor's kinetic energy. These can be cancelled by the ghosts associated with recoordinatization invariance except when one destroys that invariance by introducing a lattice (cutoff). Regulation of gravitation by a lattice cutoff leads to a funtional integral which does not cenverge on the conformal factor. Convergence of the integral can be insured by introducing a potential depending on the flat background lattice metric, but it can also be achieved by introducing higher order (curvature squared) terms in the action. Such a term together with the usual linear term selects a scale which can be used to single out a special size for the lattice. This ties together renormalization and gravitation in an interesting way. (orig.)