Non-Gaussianity from Instant and Tachyonic Preheating

We study non-Gaussianity in two distinct models of preheating: instant and tachyonic. In instant preheating non-Gaussianity is sourced by the local terms generated through the coupled perturbations of the two scalar fields. We find that the non-Gaussianity parameter is given by $f_{NL}^{\phi}\sim 2g < O(1)$, where $g$ is a coupling constant, so that instant preheating is unlikely to be constrained by WMAP or Planck. In the case of tachyonic preheating non-Gaussianity arises solely from the instability of the tachyon matter and is found to be large. We find that for single field inflation the present WMAP data implies a bound $V_{0}^{1/4}/M_{P}\leq 10^{-4}$ on the scale of tachyonic instability. We argue that the tachyonic preheating limits are useful also for string-motivated inflationary models.