Quantizing gravity with a cosmological constant

We argue that the quantization of gravity with a cosmological constant, Λ, is both necessary and feasible (in the sense that the evaluation of the functional integral is no more difficult than when Λ= 0). We illustrate this point by evaluating the one-loop counterterms and anomalous scaling behavior for pure gravity with a Λ term and for matter fieldsin an external gravitational field. Previous attempts at these calculations are found to be in error. The new results have implications for Hawking's “spacetime foam”.