A note on the role of the boundary terms for the non-Gaussianity in general k-inflation

TL;DR

This work analyzes the calculation of the leading-order bispectrum in general k-inflation models, focusing on boundary terms that arise from integrations by parts in the cubic action. By performing the computation in the comoving gauge, the authors show that total time-derivative boundary interactions cannot be assumed negligible and demonstrate that the boundary-term contribution reproduces the result obtained via the standard field-redefinition method. They find that the full bispectrum is identical whether one includes boundary terms or performs a field redefinition, providing a clear bridge between these two common approaches. The study underscores the importance of working with a canonical action free of second-order time derivatives and clarifies methodological choices in non-Gaussianity analyses for k-inflation, DBI-inflation, and related models.

Abstract

In this short note we clarify the role of the boundary terms in the calculation of the leading order tree-level bispectrum in a fairly general minimally coupled single field inflationary model, where the inflaton's Lagrangian is a general function of the scalar field and its first derivatives. This includes k-inflation, DBI-inflation and standard kinetic term inflation as particular cases. These boundary terms appear when simplifying the third order action by using integrations by parts. We perform the calculation in the comoving gauge obtaining explicitly all total time derivative interactions and show that a priori they cannot be neglected. The final result for the bispectrum is equal to the result present in the literature which was obtained using the field redefinition.