Gravitational Models with Higher Derivatives.

A class of gravitational models derived from actions which contain both the Hilbert action and two additional terms quadratic in the curvature tensor are considered at the classical and quantum mechanical levels. In addition to the usual massless excitations of the field, these models contain massive spin two and massive scalar excitations, with masses dependent upon the ratios of the coefficients of the new terms in the action to that of the Hilbert term. Specific combinations of the new terms give models with either the massive tensor or massive scalar absent. The models achieve for the first time renormalizability in a gravitational model, but at the price of either negative probabilities, a loss of unitarity, or possibly a loss of microscopic casualty.