The large-N running of the spectral index of inflation
  We extend previous classifications of inflationary models by means of their behaviour at large-N, where N is the number of e-foldings. In addition to the perturbative 1/N case, whose slow-roll parameters fall off as powers of 1/N, we introduce the constant, non-perturbative and logarithmic classes. This covers the large majority of inflationary models. Furthermore, we calculate the running of the spectral tilt for all these classes. Remarkably, we find that the tilt's runnings essentially cluster around the permil level. We comment on the implications for future experiments. 
Juan Garcia-Bellido, Diederik Roest
astro-ph.CO gr-qc hep-ph hep-th