Tensor instabilities at the end of the LCDM universe

Abstract: The unphysical spin-2 massive degrees of freedom in higher derivative gravity may be either massive unphysical ghosts or tachyonic ghosts. In the last case there is no Planck-scale threshold protecting vacuum cosmological solutions from instabilities. Within the anomaly-induced action formalism the photon-driven IR running of the coefficient of the Weyl-squared term makes the ghost eventually becoming tachyon, that should produce a gravitational explosion of vacuum. This effect is stable under higher loop corrections and takes place also in known versions of perturbative quantum gravity. However, the contribution of massless fields in the far IR are not the same in flat and de~Sitter spaces. In the asymptotically deSitter case one can observe a kind of IR decoupling, which protects the cosmological solution from the future tachyonic instabilities.