New features in curvaton model

TL;DR

This paper explores how non-linear features of the curvaton model, especially the parameters $f_{NL}$ and $g_{NL}$, are affected by specific potential features like oscillations and a single 'feature', revealing significant deviations from standard quadratic models.

Contribution

It introduces new insights into the behavior of non-linearity parameters in the curvaton model with complex potentials, highlighting their sensitivity to potential features.

Findings

$f_{NL}$ can change sign with oscillatory potential features.

$g_{NL}$ can become very large and negative.

Both parameters exhibit oscillatory behavior with potential features.

Abstract

We demonstrate novel features in the behavior of the second and third order non-linearity parameters of the curvature perturbation, namely, $f_{NL}$ and $g_{NL}$, arising from non-linear motion of curvaton field. We investigate two classes of potentials for the curvaton - the first has tiny oscillations super-imposed upon the quadratic potential. The second is characterized by a single 'feature' separating two quadratic regimes with different mass scales. The feature may either be a bump or a flattening of the potential. In the case of the oscillatory potential we find that as the width and height of superimposed oscillations increase, both $f_{NL}$ and $g_{NL}$ deviate strongly from their expected values from a quadratic potential. $f_{NL}$ changes sign from positive to negative as the oscillations in the potential become more prominent. Hence, this model can be severely constrained by convincing evidence from observations that $f_{NL}$ is positive. $g_{NL}$, on the other hand, acquires very large negative values. For the the single feature potential, we find that $f_{NL}$ and $g_{NL}$ exhibit oscillatory behavior as a function of the parameter that controls the feature.