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/d ln k ∼ 2π/ΔN (n_s - 1)) where ΔN 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.