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

TL;DR

This paper investigates the non-gaussianity of the inflaton field during inflation, showing that apparent growth outside the horizon is canceled by other effects, thus maintaining the constancy of curvature perturbations.

Contribution

It demonstrates that the N_e dependent non-gaussianity from inflaton self interactions is canceled by other non-linear effects, clarifying the behavior of _{NL} outside the horizon.

Findings

The N_e dependent term in f_{NL} is canceled by other contributions.

Non-gaussianity from inflaton self interactions is significant but does not grow outside the horizon.

Curvature perturbations remain constant outside the horizon despite non-linear interactions.

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.