Preheating and the non-gaussianity of the curvature perturbation

TL;DR

This work analyzes how preheating can generate or modify the primordial curvature perturbation ζ using the δN formalism, focusing on quadratic and quartic chaotic inflation. It distinguishes curvaton-type preheating (direct involvement of a light field in preheating) from modulated preheating (indirect via field-dependent couplings or masses) and derives general expressions for ζ, including its power spectrum and non-Gaussianity parameter f_NL. The results show that curvaton-type preheating is ineffective for the quadratic potential, while modulated preheating can be significant under suitable coupling modulation; for quartic (massless) preheating, curvaton-type contributions may exist but require modifications to the standard δN approach and rely on numerical simulations for rough estimates. The paper emphasizes the conditions under which preheating-induced ζ could be observable and outlines directions for future work, including extensions to massless preheating and potential vector-field effects.

Abstract

The perturbation of a light field might affect preheating and hence generate a contribution to the spectrum and non-gaussianity of the curvature perturbation ζ. The field might appear directly in the preheating model (curvaton-type preheating) or indirectly through its effect on a mass or coupling (modulated preheating). We give general expressions for ζbased on the δN formula, and apply them to the cases of quadratic and quartic chaotic inflation. For the quadratic case, curvaton-type preheating is ineffective in contributing to ζ, but modulated preheating can be effective. For quartic inflation, curvaton-type preheating may be effective but the usual δN formalism has to be modified. We see under what circumstances the recent numerical simulation of Bond et al. [0903.3407] may be enough to provide a rough estimate for this case. This paper is dedicated to the memory of Lev Kofman who died on 12th November 2009

Figures (3)

• Figure 1: $f_{\rm NL}$ in the plane of $\chi/M$ and $M$ in case of $g^{2} = 10^{-7}$. We plotted $f_{\rm NL} = -10^{-2}, -0.1, -1$ and $-10$ from top to bottom. The boundary ${\cal P}_{\zeta_{\sigma}} \le {\cal P}_{\zeta,{\rm obs}}$ ( $\sim 3 \times 10^{-9}$) is also plotted by the solid line.
• Figure 2: Same as Fig. \ref{['first']} but for $g^{2} = 10^{-8}$
• Figure 3: Integral half-circle and the position of the poles in the complex $\omega$ plane. The direction of the integral is denoted by arrows