Interesting features of a general class of higher-derivative theories of quantum gravity

In this work we investigate an interesting connection between the absence of Newtonian singularities in the classical nonrelativistic potential and renormalizability properties in higher-derivative models of quantum gravity. In the framework of a large class of D-dimensional higher-derivative models of quantum gravity, we compute the nonrelativistic potential energy associated with two pointlike masses. Investigating its behavior for small distances, we find an algebraic condition which is sufficient for the cancellation of the Newtonian singularity. We verify that the same condition is necessary to ensure power-counting renormalizability and, as a consequence, we conclude that renormalizable higher-derivative models do not exhibit the so-called Newtonian singularity. Finally, we discuss the role of ghosts in the mechanism for the cancellation of Newtonian singularities.