Primordial non-gaussianities from multiple-field inflation

TL;DR

This work derives the primordial three-point function for a general set of multi-field inflaton candidates at horizon crossing, providing the initial condition for the curvature perturbation’s non-Gaussianity within the Sasaki–Stewart $\delta N$ framework. By computing the horizon-crossing scalar three-point function $\mathcal{A}^{IJK}$ and relating it to $\zeta$ via $N_{,I}$, the authors show that the resulting non-Gaussianity is typically small, of order a slow-roll parameter, and can be evolved on superhorizon scales to yield the observable $f_{\mathrm{NL}}$. They verify consistency with Maldacena’s single-field result and illustrate the method with assisted inflation, where the horizon-crossing contribution aligns with a single effective-field description. The findings provide a concrete, gauge-consistent initial condition for subsequent superhorizon evolution and clarify how microphysical non-Gaussianity interacts with possible large-scale isocurvature-driven evolution. Overall, the paper advances the quantitative link between multi-field microphysics at horizon exit and the later, potentially enhanced, non-Gaussian signatures in the cosmic microwave background.

Abstract

We calculate the three-point correlation function evaluated at horizon crossing for a set of interacting scalar fields coupled to gravity during inflation. This provides the initial condition for the three-point function of the curvature perturbation in the Sasaki--Stewart δN formulation. We find that the effect is small, of the order of a slow-roll parameter, and that the non-gaussianity can be determined on large scales once the unperturbed background evolution is known. As an example of the use of our formalism, we calculate the primordial non-gaussianity arising in a model of assisted inflation.