Negative spectral index of $f_{NL}$ in the axion-type curvaton model

TL;DR

This paper analyzes the spectral index of non-Gaussianity parameter $f_{NL}$ in axion-type curvaton models, finding it to be negative and potentially detectable, which can distinguish this model from others.

Contribution

It provides a detailed numerical study of the spectral index of $f_{NL}$ in axion-type curvaton models, highlighting conditions for its negativity and potential observability.

Findings

Spectral index of $f_{NL}$ can be approximately -0.1 in the axion-type model.

Maximum negative spectral index occurs near $\sigma_*=rac{\pi f}{2}$.

Detection of positive $n_{f_{NL}}$ would exclude the axion-type curvaton model.

Abstract

We derive the spectral index of $f_{NL}$ and its running from isocurvature single field and investigate the curvaton models with a negative spectral index of $f_{NL}$ in detail. In particular, a numerical study of the axion-type curvaton model is illustrated, and we find that the spectral index of $f_{NL}$ is negative and its absolute value is maximized around $\sigma_*=\pi f/2$ for the potential $V(\sigma)=m^2f^2(1-\cos{\sigma\over f})$. The spectral index of $f_{NL}$ can be ${\cal O}(-0.1)$ for the axion-type curvaton model. A convincing detection of a positive $n_{f_{NL}}$ 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.