Running spectral index from large-field inflation with modulations revisited

We revisit large field inflation models with modulations in light of the recent discovery of the primordial B-mode polarization by the BICEP2 experiment, which, when combined with the Planck+WP+highLPlanck+WP+highL data, gives a strong hint for additional suppression of the CMB temperature fluctuations at small scales. Such a suppression can be explained by a running spectral index. In fact, it was pointed out by two of the present authors (TK and FT) that the existence of both tensor mode perturbations and a sizable running of the spectral index is a natural outcome of large inflation models with modulations such as axion monodromy inflation. We find that this holds also in the recently proposed multi-natural inflation, in which the inflaton potential consists of multiple sinusoidal functions and therefore the modulations are a built-in feature.