Primordial Non-Gaussianities of General Multiple Field Inflation

TL;DR

This paper analyzes the primordial non-Gaussianities in general multi-field inflation models, providing a comprehensive calculation of the three-point function and showing how non-Gaussianity depends on slow-varying parameters.

Contribution

It generalizes previous results by deriving the cubic action and three-point function for multi-field inflation with a broad class of Lagrangians.

Findings

Non-Gaussianity is determined by slow-varying parameters and model structure.

Results apply to models with sound speed close to one.

Provides a framework for future multi-field inflation studies.

Abstract

We perform a general study of the primordial scalar non-Gaussianities in multi-field inflationary models in Einstein gravity. We consider models governed by a Lagrangian which is a general function of the scalar fields and their first spacetime derivatives. We use $\delta N$ formalism to relate scalar fields and curvature perturbations. We calculate the explicit cubic order perturbation action and the three-point function of curvature perturbation evaluated at horizon-crossing. Under reasonable assumptions, in the limit of small slow-varying parameters and a sound speed $c_s$ close to one, we find that the non-Gaussianity is completely determined by these slow-varying parameters and some other parameters determined by the structure of the inflationary models. Our work generalizes previous results, and would be useful to study non-Gaussianity in multi-field inflationary models that will be constructed in the future.