  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 + 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.
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.
