Revisiting non-Gaussianity in multifield inflation with curved field space

TL;DR

This paper derives a comprehensive cubic action for non-Gaussianities in two-field inflation models with curved field space, enabling analytical studies and highlighting observable effects from non-canonical kinetic terms.

Contribution

It provides the complete cubic action in comoving gauge for two-field inflation with curved field space, facilitating analytical approximations and deriving an effective single-field theory.

Findings

Derived the cubic action in terms of observable quantities.

Showed the scaling of operators with slow-roll parameters.

Formulated an effective single-field theory for heavy entropic modes.

Abstract

Recent studies of inflation with multiple scalar fields have highlighted the importance of non-canonical kinetic terms in novel types of inflationary solutions. This motivates a thorough analysis of non-Gaussianities in this context, which we revisit here by studying the primordial bispectrum in a general two-field model. Our main result is the complete cubic action for inflationary fluctuations written in comoving gauge, i.e. in terms of the curvature perturbation and the entropic mode. Although full expressions for the cubic action have already been derived in terms of fields fluctuations in the flat gauge, their applicability is mostly restricted to numerical evaluations. Our form of the action is instead amenable to several analytical approximations, as our calculation in terms of the directly observable quantity makes manifest the scaling of every operator in terms of the slow-roll parameters, what is essentially a generalization of Maldacena's single-field result to non-canonical two-field models. As an important application we derive the single-field effective field theory that is valid when the entropic mode is heavy and may be integrated out, underlining the observable effects that derive from a curved field space.