  Understanding the role of higher derivatives is probably one of the most
relevant questions in quantum gravity theory. Already at the semiclassical
level, when gravity is a classical background for quantum matter fields, the
action of gravity should include fourth derivative terms to provide
renormalizability in the vacuum sector. The same situation holds in the quantum
theory of metric. At the same time, including the fourth derivative terms means
the presence of massive ghosts, which are gauge-independent massive states with
negative kinetic energy. At both classical and quantum level such ghosts
violate stability and hence the theory becomes inconsistent. Several approaches
to solve this contradiction were invented and we are proposing one more, which
looks simpler than those what were considered before. We explore the dynamics
of the gravitational waves on the background of classical solutions and give
certain arguments that massive ghosts produce instability only when they are
present as physical particles. At least on the cosmological background one can
observe that if the initial frequency of the metric perturbations is much
smaller than the mass of the ghost, no instabilities are present.
