Remarks on non-gaussian fluctuations of the inflaton and constancy of \zeta outside the horizon

Abstract

We point out that the non-gaussianity arising from cubic self interactions of the inflaton field is proportional to \xi N_e where \xi ~ V"' and N_e is the number of e-foldings from horizon exit till the end of inflation. For scales of interest N_e = 60, and for models of inflation such as new inflation, natural inflation and running mass inflation \xi is large compared to the slow roll parameter \epsilon ~ V'^{2}. Therefore the contribution from self interactions should not be outrightly ignored while retaining other terms in the non-gaussianity parameter f_{NL}. But the N_e dependent term seems to imply the growth of non-gaussianities outside the horizon. Therefore we briefly discuss the issue of the constancy of correlations of the curvature perturbation \zeta outside the horizon. We then calculate the 3-point function of the inflaton fluctuations using the canonical formalism and further obtain the 3-point function of \zeta_k. We find that the N_e dependent contribution to f_{NL} from self interactions of the inflaton field is cancelled by contributions from other terms associated with non-linearities in cosmological perturbation theory.