Primordial Non-Gaussianities of General Multiple Field Inflation

TL;DR

The paper tackles how primordial non-Gaussianities arise in broad multi-field inflation models with non-canonical kinetic terms, using a general P(X, φ^I) framework. It develops a comprehensive perturbative approach based on the δN formalism to relate curvature perturbations to multi-field fluctuations and computes the cubic action and horizon-crossing three-point function, valid to leading slow-varying order with $c_s$ near unity. The main finding is that the non-Gaussianity parameter $f_{NL}$ is controlled by slow-varying parameters and a model-dependent combination $\lambda$, with prospects for large $f_{NL}$ when $|\lambda/(H^2 ε)|$ is large or when $c_s$ deviates from 1; canonical limits recover known results. The work provides a general framework for analyzing multi-field non-Gaussianity in future inflationary constructions and connects horizon-crossing physics to potential post-inflationary evolution of perturbations.

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 $δN$ 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.