On non-Gaussianities in multi-field inflation (N fields): bi- and tri-spectra beyond slow-roll

We compute analytic expressions for the non-linearity parameters characterizing the bi- and tri-spectrum of primordial curvature perturbations generated during an inflationary epoch of the early universe driven by an arbitrary number fields. We assume neither slow roll nor a separable potential; instead, to compute Non-Gaussianities, we assume a separable Hubble parameter. We apply the formalism to an exact solvable toy-model and show under which conditions observably large non-Gaussianities are produced.