Remarks on non-Gaussian fluctuations of the inflaton and constancy of ζ outside the horizon

Abstract

We have pointed out that the non-Gaussianity arising from cubic self interactions of the inflaton field is proportional to ξNe. For scales of interest Ne = 60, and for models such as new inflation, natural inflation, and running mass inflation ξ is large compared to the slow roll parameter. Therefore, the contribution from self interactions should not be outrightly ignored while retaining other terms in the non-Gaussianity parameter fNL. But the Ne dependent term seems to imply the growth of non-Gaussianities outside the horizon. Therefore, we have briefly discussed the issue of the constancy of correlations of the curvature perturbation ζ outside the horizon. We have then presented our results on the 3-point function of ζk, and found that the Ne dependent contribution to fNL from self interactions of the inflaton field is cancelled by contributions from other terms associated with non-linearities in cosmological perturbation theory.