  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
$\lambda\phi^4$ potential which is governing the expansion of the Universe. A
second field $\sigma$, coupled to the inflaton through $g^2\phi^2\sigma^2$, is
excited from the vacuum fluctuations. The excited modes of $\sigma$ 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, $1<
g^2/\lambda < 3$, the non-Gaussianity parameter becomes: $f_{NL}\geq {\cal
O}(1000)$, which is already ruled out by the current WMAP observation.

Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory