Very Large Primordial Non-Gaussianity from multi-field: Application to Massless Preheating

TL;DR

The paper develops a general, local second-order formalism for the curvature perturbation in multi-field inflation with a single-field-dominated background and applies it to massless preheating with a quartic inflaton potential coupled to a second field. The analysis demonstrates that isocurvature fluctuations can excite large second-order curvature perturbations, yielding $f_{NL}$ of order $10^3$ within the band $1< g^2/\lambda < 3$, already ruled out by observations. This work highlights massless preheating as a stringent testbed for early-Universe dynamics and shows how non-Gaussianity can serve as a powerful discriminator among preheating scenarios. The findings motivate further numerical studies of multi-field preheating to tighten constraints on model parameters and to map the associated non-Gaussian signatures.

Abstract

In this paper we derive a generic expression, which is valid for scales larger than Hubble radius and contains only the local terms, for the second order curvature perturbations for more than one field, provided the expansion is sourced by the energy density of a single field. As an application, motivated by our previous paper [1], we apply our formalism to two fields during preheating, where the inflaton oscillations are sourced by $λφ^4$ potential which is governing the expansion of the Universe. A second field $σ$, coupled to the inflaton through $g^2φ^2σ^2$, is excited from the vacuum fluctuations. The excited modes of $σ$ amplify the super-Hubble isocurvature perturbations, which seed the second order curvature perturbations to give rise to a significantly large non-Gaussianity. Our results show that within 3 inflaton oscillations for a range of parameters, $1< g^2/λ< 3$, the non-Gaussianity parameter becomes: $f_{NL}\geq {\cal O}(1000)$, which is already ruled out by the current WMAP observation.

Figures (2)

• Figure 1: The evolution of the non-Gaussianity parameter, $f_{NL}$, with different values of $g^2/\lambda=1.2,\,1.5,\,1.875$ with red, green and blue lines. $g^2/\lambda=1.875$ is the case with largest characteristic exponent. The end point corresponds to 3 oscillations of the inflaton and at that point the largest $-f_{NL}=1382$.
• Figure 2: The same as previous figure with $g^2/\lambda=1.875,\,2,\,2.5$ with blue, green and red lines. The cases with $g^2/\lambda=1.875$ (blue) and $2$ (green) produce almost identical results, which is not surprising since $\mu_{1.875}\approx 0.238$ and $\mu_2\approx 0.236$.