The spectral index and its running in axionic curvaton

We show that a sizable running spectral index suggested by the recent SPT data can be explained in the axionic curvaton model with a potential that consists of two sinusoidal contributions of different height and period. We find that the running spectral index is generically given by dn(s)/dln k similar to 2 pi/Delta N(n(s) - 1), where Delta N is the e-folds during one period of modulations. In the string axiverse, axions naturally acquire a mass from multiple contributions, and one of the axions may be responsible for the density perturbations with a sizable running spectral index via the curvaton mechanism. We note that the axionic curvaton model with modulations can also accommodate the red-tilted spectrum with a negligible running, without relying on large-field inflation.