Stability of flat space, semiclassical gravity, and higher derivatives

Flat space is shown to be perturbatively stable, to first order in $\hslash$, against quantum fluctuations produced in semiclassical (or $\frac{1}{N}$ expansion) approximations to quantum gravity, despite past indications to the contrary. It is pointed out that most of the new "solutions" allowed by the semiclassical corrections do not fall within the perturbative framework, unlike the effective action and field equations which generate them. It is shown that excluding these nonperturbative "pseudosolutions" is the only self-consistent approach. The remaining physical solutions do fall within the perturbative formalism, do not require the introduction of new degrees of freedom, and suffer none of the pathologies of unconstrained higher-derivative systems. As a demonstration, a simple model is solved, for which the correct answer is not obtained unless the nonperturbative pseudosolutions are excluded. The presence of the higher-derivative terms in the semiclassical corrections may be related to nonlocality.