Non-gaussianity from the bispectrum in general multiple field inflation

TL;DR

The article advances understanding of non-Gaussianity in multifield inflation with a general kinetic term by deriving the full second- and third-order actions, including metric perturbations, and decomposing perturbations into adiabatic and entropy modes. It shows that adiabatic and entropy sound speeds $c_{ad}$ and $c_{en}$ are generally distinct and can be $<1$, enhancing the bispectrum, with DBI-inflation yielding $c_{ad}=c_{en}$. The leading slow-roll bispectrum includes both pure adiabatic and mixed adiabatic-entropy contributions, which can have different momentum dependencies, offering a diagnostic to distinguish multifield models from single-field ones; in the DBI limit, entropy effects primarily adjust amplitude, potentially relaxing DBI constraints. The results provide a framework to interpret CMB non-Gaussianity in the context of general multifield theories and to identify observational signatures that differentiate K-inflation, DBI-inflation, and more general kinetic structures.

Abstract

We study the non-gaussianity from the bispectrum in multi-field inflation models with a general kinetic term. The models include the multi-field K-inflation and the multi-field Dirac-Born-Infeld (DBI) inflation as special cases. We find that, in general, the sound speeds for the adiabatic and entropy perturbations are different and they can be smaller than 1. Then the non-gaussianity can be enhanced. The multi-field DBI-inflation is shown to be a special case where both sound speeds are the same due to a special form of the kinetic term. We derive the exact second and third order actions including metric perturbations. In the small sound speed limit and at leading order in the slow-roll expansion, we derive the three point function for the curvature perturbation which depends on both adiabatic and entropy perturbations. The contribution from the entropy perturbations has a different momentum dependence if the sound speed for the entropy perturbations is different from the adiabatic one, which provides a possibility to distinguish the multi-field models from single field models. On the other hand, in the multi-field DBI case, the contribution from the entropy perturbations has the same momentum dependence as the pure adiabatic contributions and it only changes the amplitude of the three point function. This could help to ease the constraints on the DBI-inflation models.