Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Non-Gaussianity in Curvaton Models with Nearly Quadratic Potential

Kari Enqvist, Sami Nurmi

TL;DR

This paper investigates how small departures from a purely quadratic curvaton potential affect primordial non-Gaussianity. Using the separate-universe framework, the authors derive the curvature perturbation $\zeta$ to second order and show that the non-Gaussianity parameter $f_{NL}$ acquires a potential-dependent term that vanishes for a strictly quadratic potential. By introducing a near-quadratic self-interaction $\lambda m^{4-n}_{\sigma}\sigma^n$, they compute the induced corrections to the curvaton oscillation amplitude and obtain an analytic expression for $f_{NL}$, revealing that $|f_{NL}|$ can be suppressed (or enhanced) relative to the quadratic case depending on the exponent $n$ and the correction size $s$. In the limit of small curvaton energy density $r\ll1$, the potential correction can allow $|f_{NL}|$ to be much less than unity, relaxing the usual lower bound on $r$ and showing that current non-Gaussianity constraints do not generically rule out curvaton models without specifying higher-order terms in the potential.

Abstract

We consider curvaton models with potentials that depart slightly from the quadratic form. We show that although such a small departure does not modify significantly the Gaussian part of the curvature perturbation, it can have a pronounced effect on the level of non-Gaussianity. We find that unlike in the quadratic case, the limit of small non-Gaussianity, $|f_{NL}|\ll1$, is quite possible even with small curvaton energy density $r\ll1$ . Furthermore, non-Gaussianity does not imply any strict bounds on $r$ but the bounds depend on the assumptions about the higher order terms in the curvaton potential.

Non-Gaussianity in Curvaton Models with Nearly Quadratic Potential

TL;DR

This paper investigates how small departures from a purely quadratic curvaton potential affect primordial non-Gaussianity. Using the separate-universe framework, the authors derive the curvature perturbation to second order and show that the non-Gaussianity parameter acquires a potential-dependent term that vanishes for a strictly quadratic potential. By introducing a near-quadratic self-interaction , they compute the induced corrections to the curvaton oscillation amplitude and obtain an analytic expression for , revealing that can be suppressed (or enhanced) relative to the quadratic case depending on the exponent and the correction size . In the limit of small curvaton energy density , the potential correction can allow to be much less than unity, relaxing the usual lower bound on and showing that current non-Gaussianity constraints do not generically rule out curvaton models without specifying higher-order terms in the potential.

Abstract

We consider curvaton models with potentials that depart slightly from the quadratic form. We show that although such a small departure does not modify significantly the Gaussian part of the curvature perturbation, it can have a pronounced effect on the level of non-Gaussianity. We find that unlike in the quadratic case, the limit of small non-Gaussianity, , is quite possible even with small curvaton energy density . Furthermore, non-Gaussianity does not imply any strict bounds on but the bounds depend on the assumptions about the higher order terms in the curvaton potential.

Paper Structure

This paper contains 6 sections, 18 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The curvature perturbation generated in the curvaton model
  3. Small deviation from the quadratic potential
  4. The behaviour of $|f_{NL}|$ in the limit $r\ll1$
  5. Restrictions on the potential correction
  6. Conclusions

Figures (2)

  • Figure 1: The non-linearity parameter $|f_{NL}|$ in units $5/3r=1$ as a contourplot with $n=4$ on the left panel and $n=6$ on the right panel. The scale on y-axis is logarithmic. The values of $|f_{NL}|$ are evaluated only in the perturbative region $s\lesssim2/n$ and the non-perturbative region is printed in white.
  • Figure 2: Allowed regions in the parameter space $(s,r)$. The labels are outside the allowed region for a given value of $n$.