On the stability of the anomaly-induced inflation
  We analyze various phases of inflation based on the anomaly-induced effective action of gravity (modified Starobinsky model), taking the cosmological constant Lambda and k=0, +/- 1 topologies into account. The total number of the inflationary e-folds may be enormous, but at the last 65 of them the inflation greatly slows down due to the contributions of the massive particles. For the supersymmetric particle content, the stability of inflation holds from the initial point at the sub-Planck scale until the supersymmetry breaks down. After that the universe enters into the unstable regime with the eventual transition into the stable FRW-like evolution with small positive cosmological constant. It is remarkable, that all this follows automatically, without fine-tuning of any sort, independent on the values of Lambda and k. Finally, we consider the stability under the metric perturbations during the last 65 e-folds of inflation and find that the amplitude of the ones with the wavenumber below a certain cutoff has an acceptable range. 
A.M. Pelinson, I.L. Shapiro and F.I. Takakura