Stability issues in Euclidean quantum gravity

It is known that the action of Euclidean Einstein gravity is not bounded from below and that the metric of flat space does not correspond to a minimum of the action. Nevertheless, perturbation theory about flat space works well. The deep dynamical reasons for this reside in the nonperturbative behavior of the system and have been clarified in part by numerical simulations. Several open issues remain. We treat in particular those zero modes of the action for which $R\left(x\right)\mathrm{}$ is not identically zero, but the integral of $\sqrt{g\left(x\right)\mathrm{}}R\left(x\right)\mathrm{}$ vanishes.