Runnings in the Curvaton

TL;DR

This paper analyzes the scale-dependence of density perturbations and non-Gaussianity in various curvaton models, providing analytic formulas and classifying potentials based on their effects on fNL running.

Contribution

It introduces analytic expressions for the runnings of perturbations in general curvaton potentials and classifies potential types based on their influence on fNL scale dependence.

Findings

Second order perturbations can be strongly scale-dependent.

Potential flattening or steepening affects fNL running significantly.

Multi-source models can produce large fNL scale dependence.

Abstract

We investigate the scale-dependence, or the runnings, of linear and second order density perturbations generated in various curvaton scenarios. We argue that the second order perturbations, i.e. non-Gaussianity, can strongly depend on the scale, even when the linear perturbations are nearly scale-invariant. We present analytic formulae for the runnings from curvatons with general energy potentials, and clarify the conditions under which fNL becomes strongly scale-dependent. From the point of view of the fNL running, curvaton potentials can be classified into roughly two categories by whether the potential flattens or steepens compared to a quadratic one. As such examples, we study pseudo-Nambu-Goldstone curvatons, and self-interacting curvatons, respectively. The dynamics of non-quadratic curvatons and the behaviors of the resulting density perturbations are clarified by analytical methods. Then we also study models where multiple source can be responsible for density perturbations such as the multi-curvaton, and mixed curvaton and inflaton models where the running of fNL can also be large due to their multi-source nature. We make quantitative analysis for each curvaton scenario and discuss in what cases the scale-dependence, in particular, of fNL can be large enough to be probed with future CMB experiments.