Non-Gaussianity from the bispectrum in general multiple field inflation

Abstract

We study the non-Gaussianity from the bispectrum in multi-field inflation models with ageneral kinetic term. The models include multi-field K-inflation and multi-fieldDirac–Born–Infeld (DBI) inflation as special cases. We find that, in general, the soundspeeds for the adiabatic and entropy perturbations are different and they canbe smaller than 1. Then the non-Gaussianity can be enhanced. Multi-field DBIinflation is shown to be a special case where both sound speeds are the samedue to a special form of the kinetic term (Langlois et al 2008 Preprint 0804.3139[hep-th]). We derive the exact second-and third-order actions including metricperturbations. In the small sound speed limit and at leading order in the slow-rollexpansion, we derive the three-point function for the curvature perturbation whichdepends on both adiabatic and entropy perturbations. The contribution fromthe entropy perturbations has a different momentum dependence if the soundspeeds for the entropy and adiabatic perturbations are different, which provides apossibility to distinguish multi-field models from single-field models. On the otherhand, in the multi-field DBI case, the contribution from the entropy perturbationshas the same momentum dependence as the pure adiabatic contributions andit only changes the amplitude of the three-point function (Langlois et al 2008Preprint 0804.3139 [hep-th]). This could help to ease the constraints on the DBI-inflationmodels.