Primordial Non-Gaussianity in Multi-Scalar Slow-Roll Inflation

TL;DR

The paper develops a general framework to compute primordial non-Gaussianity in multi-scalar slow-roll inflation using the δN formalism, without assuming separable potentials. It derives a concise analytic expression for the nonlinear parameter $f_{NL}$ in terms of background quantities and an integral over the inflationary trajectory, showing that $f_{NL}$ is typically suppressed by slow-roll but can acquire order-one enhancements from evolution. Under relaxed slow-roll conditions, large non-Gaussianity requires departing from standard slow-roll or having sizable higher-derivative contributions, particularly in directions orthogonal to the background trajectory. The results extend previous single-field and separable-potential analyses and provide a practical method to test multi-field models against observational constraints.

Abstract

We analyze the non-Gaussianity for primordial curvature perturbations generated in multi-scalar slow-roll inflation model including the model with non-separable potential by making use of $δN$ formalism. Many authors have investigated the possibility of large non-Gaussianity for the models with separable potential, and they have found that the non-linear parameter, $f_{NL}$, is suppressed by the slow-roll parameters. We show that for the non-separable models $f_{NL}$ is given by the product of a factor which is suppressed by the slow-roll parameters and a possible enhancement factor which is given by exponentials of quantities of O(1).