Curvaton Dynamics and the Non-Linearity Parameters in Curvaton Model

TL;DR

The paper investigates how small departures from a quadratic curvaton potential modify local-type non-Gaussianity, focusing on the second and higher-order non-linearity parameters $f_{NL}$ and $g_{NL}$. By modeling the potential as $V(\ olinebreak[4] \sigma) = \frac{1}{2} m^2 \sigma^2 + \lambda m^4 (\sigma/m)^n$ with a dimensionless deviation $s = \lambda (\sigma_*/m)^{n-2}$, the authors derive a perturbative framework linking post-inflation dynamics to $f_{NL}$ and $g_{NL}$ through functions $w(x_o)$ and $g(n,x_o)$ and show that negative $s$ (e.g., axion-type curvatons) can yield large $g_{NL}$ even when $f_{NL}$ is large. They introduce an observable alpha$ (s) to quantify the self-interaction and demonstrate that $g_{NL}$ scales with $f_{NL}^2$ for $s<0$, with $ au_{NL}$ similarly related, while a positive $s$ can suppress $f_{NL}$. The work provides practical estimates for the coupling $\lambda$ and shows that upcoming experiments like Planck could detect these signatures, potentially favoring axion-type curvatons if a large positive $g_{NL}$ is observed.

Abstract

We investigate the curvaton dynamics and the non-linearity parameters in curvaton model with potential slightly deviating from the quadratic form in detail. The non-linearity parameter $g_{NL}$ will show up due to the curvaton self-interaction. We also point out that the leading order of non-quadratic term in the curvaton potential can be negative, for example in the axion-type curvaton model. If a large positive $g_{NL}$ is detected, the axion-type curvaton model will be preferred.

Figures (1)

• Figure 1: The values of $w(x_o)$ and $g(n,x_o)$ for different $x_o$.