Negative spectral index of fNL in the axion-type curvaton model

We derive the spectral index of fNL and its running from isocurvature single field and investigate the curvaton models with a negative spectral index of fNL in detail. In particular, a numerical study of the axion-type curvaton model is illustrated, and we find that the spectral index of fNL is negative and its absolute value is maximized around σ* = πf/2 for the potential V(σ) = m2f2(1−cos (σ/f)). The spectral index of fNL can be O(−0.1) for the axion-type curvaton model. A convincing detection of a positive nfNL will rule out the axion-type curvaton model. In addition, we also give a general discussion about the detectable parameter space for the curvaton model with a polynomial potential