Non-Gaussianities in Multi-field Inflation

Abstract

We compute the amplitude of the non-Gaussianities in inflationary models with multiple, uncoupled scalar fields. This calculation thus applies to all models of assisted inflation, including N-flation, where inflation is driven by multiple axion fields arising from shift symmetries in a flux stabilized string vacuum. The non-Gaussianities are associated with nonlinear evolution of the field (and density) perturbations, characterized by the parameter $f_{NL}$. We derive a general expression for the nonlinear parameter, incorporating the evolution of perturbations after horizon-crossing. This is valid for arbitrary separable potentials during slow roll. To develop an intuitive understanding of this system and to demonstrate the applicability of the formalism we examine several cases with quadratic potentials: two-field models with a wide range of mass ratios, and a general N-field model with a narrow mass spectrum. We uncover that $f_{NL}$ is suppressed as the number of e-foldings grows, and that this suppression is increased in models with a broad spectrum of masses. On the other hand, we find no enhancement to $f_{NL}$ that increases with the number of fields. We thus conclude that the production of a large non-Gaussian signal in multi-field models of inflation is very unlikely as long as fields are slowly rolling and potentials are of simple, quadratic form. Finally, we compute a spectrum for the scalar spectral index that incorporates the nonlinear corrections to the fields' evolution.