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 shiftsymmetries in a flux stabilized string vacuum. The non-Gaussianities are associated withnonlinear evolution of the field (and density) perturbations, characterized by the parameterfNL. We derive a general expression for the nonlinear parameter, incorporating the evolution ofperturbations after horizon-crossing. This is valid for arbitrary separable potentialsduring slow roll. To develop an intuitive understanding of this system and todemonstrate the applicability of the formalism we examine several cases with quadraticpotentials: two-field models with a wide range of mass ratios, and a general -field model with a narrow mass spectrum. We uncover thatfNL is suppressed as the number of e-foldings grows, and that this suppression is increased inmodels with a broad spectrum of masses. On the other hand, we find no enhancement tofNL that increases with the number of fields. We thus conclude that the production of a largenon-Gaussian signal in multi-field models of inflation is very unlikely as long as fields areslowly rolling and potentials are of simple, quadratic form. Finally, we compute anexpression for the scalar spectral index that incorporates the nonlinear corrections to thefields’ evolution.