Revised $f_{\rm NL}$ parameter in Curvaton Scenario

TL;DR

This paper revises the calculation of non-Gaussianity in the curvaton scenario using a generalized $ abla N$ formalism, unifying different energy dominance periods and applying it to various models including chaotic and Pseudo-Nambu-Goldstone curvatons.

Contribution

It introduces a unified method to compute $f_{NL}$ across different curvaton models and cosmological periods, improving accuracy and applicability.

Findings

Most parameter space of quadratic curvaton models aligns with observations.

The second inflationary phase for Pseudo-Nambu-Goldstone curvaton is observationally excluded.

The new formalism recovers known $f_{NL}$ values without nonlinear evolution effects.

Abstract

We revise the Non-Gaussianity of canonical curvaton scenario with a generalized $\delta N$ formalism, in which it could handle the generic potentials. In various curvaton models, the energy density is dominant in different period including the secondary inflation of curvaton, matter domination and radiation domination. Our method could unify to deal with these periods since the non-linearity parameter $f_{\rm NL}$ associated with Non-Gaussianity is a function of equation of state $w$. We firstly investigate the most simple curvaton scenario, namely the chaotic curvaton with quadratic potential. Our study shows that most parameter space satisfies with observational constraints. And our formula will nicely recover the well-known value of $f_{\rm NL}$ in the absence of non-linear evolution. From the micro origin of curvaton, we also investigate the Pseudo-Nambu-Goldstone curvaton. Our result clearly indicates that the second short inflationary process for Pseudo-Nambu-Goldstone curvaton is ruled out in light of observations. Finally, our method sheds a new way for investigating the Non-Gaussianity of curvaton mechanism, espeically for exploring the Non-Gaussianity in MSSM curvaton model.