Abstract: We explore the dynamics of metric perturbations (gravitational waves) on the cosmological background in the theory with higher derivatives and semiclassical non-local corrections coming from massless conformal fields. It is shown, by means of analytical and numerical methods that there are no growing modes until the background has enegies of Planck order of magnitude. This result means, also, that there are good chances to construct renormalizable theory of quantum gravity which is unitary for the energies below Planck scale.