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We revisit large field inflation models with modulations in light of therecent discovery of the primordial B-mode polarization by the BICEP2experiment, which, when combined with the Planck + WP + highL data, gives astrong hint for additional suppression of the CMB temperature fluctuations atsmall 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 theexistence of both tensor mode perturbations and a sizable running of thespectral index is a natural outcome of large inflation models with modulations.We find that this holds also in the recently proposed multi-natural inflation,in which the inflaton potential consists of multiple sinusoidal functions andtherefore the modulations are a built-in feature.

Running Spectral Index from Large-field Inflation with Modulations Revisited