We compute the covariant three-point function near horizon-crossing for a system of slowly-rolling scalar fields during an inflationary epoch, allowing for an arbitrary field-space metric. We show explicitly how to compute its subsequent evolution using a covariantized version of the separate universe or delta-N expansion, which must be augmented by terms measuring curvature of the field-space manifold, and give the nonlinear gauge transformation to the comoving curvature perturbation. Nonlinearities induced by the field-space curvature terms are a new and potentially significant source of non-Gaussianity. We show how inflationary models with non-minimal coupling to the spacetime Ricci scalar can be accommodated within this framework. This yields a simple toolkit allowing the bispectrum to be computed in models with non-negligible field-space curvature.
We study the evolution of non-Gaussianity in multiple-field inflationary models, focusing on three fundamental questions: (a) How is the sign and peak magnitude of the non-linearity parameter fNL related to generic features in the inflationary potential? (b) How sensitive is fNL to the process by which an adiabatic limit is reached, where the curvature perturbation becomes conserved? (c) For a given model, what is the appropriate tool -- analytic or numerical -- to calculate fNL at the adiabatic limit? We summarise recent results obtained by the authors and further elucidate them by considering an inflection point model.
We study inflationary perturbations in multiple-field models, for which zeta typically evolves until all isocurvature modes decay--the adiabatic limit. We use numerical methods to explore the sensitivity of the nonlinear parameter fNL to the process by which this limit is achieved, finding an appreciable dependence on model-specific data such as the time at which slow-roll breaks down or the timescale of reheating. In models with a sum-separable potential where the isocurvature modes decay before the end of the slow-roll phase we give an analytic criterion for the asymptotic value of fNL to be large. Other examples can be constructed using a waterfall field to terminate inflation while fNL is transiently large, caused by descent from a ridge or convergence into a valley. We show that these two types of evolution are distinguished by the sign of the bispectrum, and give approximate expressions for the peak fNL.
