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

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