Spectral index and running of $g_{NL}$ from an isocurvature scalar field

TL;DR

This paper derives the spectral index and running of the non-Gaussianity parameter $g_{NL}$ from an isocurvature scalar field, highlighting its potential detectability and applying findings to the curvaton model.

Contribution

It provides the first derivation of the spectral index and running of $g_{NL}$ for an isocurvature scalar field, including implications for the curvaton model.

Findings

Spectral index and running of $g_{NL}$ depend on the isocurvature field mass.

Detectability of scale dependence if the field mass is comparable to the Hubble parameter.

Application to the curvaton model with near quadratic potential.

Abstract

It is possible that the primordial non-Gaussianity is dominated by the higher order terms, such as that set by $g_{NL}$, not $f_{NL}$. In this paper we derive the spectral index and running of $g_{NL}$ from a single isocurvature scalar field. The scale dependences of non-Gaussianity parameters are detectable if the mass of isocurvature field is not too small compared to the Hubble parameter during inflation. In addition, we also apply our results to investigate the curvaton model with near quadratic potential in detail.