Primordial non-Gaussianities of general multiple-field inflation

We perform a general study of the primordial scalar non-Gaussianities in multi-field inflationary models in Einstein gravity. We consider models governed by a Lagrangian which is a general function of the scalar fields and their first-order spacetime derivatives. We use delta N formalism to relate scalar fields and the curvature perturbations. We calculate the explicit cubic order perturbative action and the three-point function of curvature perturbation evaluated at the horizon crossing. Under reasonable assumptions, in the small slowly varying parameters limit and with a sound speed c(s) close to one, we find that the non-Gaussianity is completely determined by these slowly varying parameters and some other parameters which are determined by the structure of the inflationary model. Our work generalizes previous results, and implies the possibility of the existence of large non-Gaussianity in model constructing, and it would be also useful to study the non-Gaussianity in multi-field inflationary models which will be constructed in the future.