Renormalization and stability in higher derivative models of quantum gravity

The main difficulty of perturbative quantum gravity (QG) in 4d is related to the conflict between renormalizability and unitarity. The simplest version of QG is based on General Relativity and is non-renormalizable. One can construct renormalizable and even superrenormalizable versions of QG by introducing higher derivatives, but the price to pay is high: one has to tolerate the presence of unphysical higher derivative massive ghosts. There are several ideas of how this contradiction can be resolved and the purpose of the talk is to review them. The list includes, in particular, taking into account the loop corrections to the propagator and also using the non-polynomial in derivatives theories of QG. On the other
hands, the dynamics of metric perturbations (gravitational waves) provides certain indications that the ghosts are actually not generated below the mass threshold, which is typically of the Planck order of magnitude. If this is true, the higher derivative models of QG can be seen as perfect theories below the Planck cut-off.