Nuclear Physics B269 (1986) 712-743 North-Holland, Amsterdam SIMPLICIAL QUANTUM GRAVITY WITH HIGHER DERIVATIVE TERMS: FORMALISM AND NUMERICAL RESULTS IN FOUR DIMENSIONS

The study of higher derivative gravity theories dates back to more than thirty years ago (for a historical review see ref. [1D. It has been known for some time that if one attempts to quantize the Einstein theory of gravity one encounters two major difficulties. The field equations for the metric are derived from an action that is unbounded from below, and the path integral is therefore mathematically ill-defined. Furthermore the coupling constant in Einstein gravity (Newton's constant) has dimension of inverse mass squared (in units h = c = 1), and this leads to a nonrenormalizable quantum theory, as can be verified by doing explicit Feynman diagram perturbation theory [2-4]. One possible attitude is to hope that these problems will be cured in the context of a grand unified theory like supergravity. Alternatively, one might argue that the above problems hint at a fundamental incompatibility between gravity and quantum mechanics, and any modification of the Einstein action will in general lead to new undetermined parameters. Of course the argument about naturalness and simplicity of the Einstein theory can be turned around, in the sense that a quantum theory of gravity should just provide the answer for why, starting with the most general microscopic theory consistent with general invariance principles, some terms appear in the low-energy