The study of stability of gravitational perturbations in higher derivative gravity has shown that at the linear level the massive unphysical ghost is not generated from vacuum if the initial seed of metric perturbation has frequency essentially below the Planck threshold. The mathematical knowledge indicated that the linear stability is supposed to hold even at the nonperturbative level, but in such a complicated case it is important to perform a verification of this statement. We compare the asymptotic stability solutions at the linear and full nonperturbative levels for the Bianchi-I metric with small anisotropies, which can be regarded as an extreme, zero frequency limit of a gravitational wave. As one should expect from the combination of previous analysis and general mathematical theorems, there is a good correspondence between linear stability and the nonperturbative asymptotic behavior.

The dynamics of cosmological anisotropies is investigated for Bianchi type I universe filled by a relativistic matter represented by the reduced relativistic gas model (RRG), with equation of state interpolating between radiation and matter. Previously it was shown that the interpolation is observed in the background cosmological solutions for homogeneous and isotropic universe and also for the linear cosmological perturbations. We extend the application of RRG to the Bianchi type I anisotropic model and find that the solutions evolve to the isotropic universe with the pressureless matter contents.