The presence of higher derivatives in the gravitational action is required for 
renormalizability in semiclassical and quantum gravity.  On the other hand, 
higher derivatives produce unphysical massive ghosts, making classical 
solutions unstable and quantum theory non-unitary. Trying to resolve this 
contradiction, we explore classical cosmological solutions in the presence 
of ghosts and find out that instability takes place only if the seeds of initial 
perturbations are about the Planck order of magnitude, such that the ghost 
can be generated from the vacuum. In the superrenormalizable versions of 
quantum gravity, there may be a pair of complex conjugate massive poles. 
In this case, it is possible that the complex ghost-like states form normal 
bound states. For a while, this mechanism was achieved only for a simplified 
toy model that reproduces the general structure of the ghost-like poles. This 
model is far from the real quantum gravity. However, assuming that the same 
situation takes place for quantum gravity, such a mechanism explains the 
existence of the Planck-scale cut-off for the frequencies of gravitational 
perturbations, and potentially resolve the problem of ghosts.