Revisiting non-Gaussianity of multiple-field inflation from the field equation

In the present paper, we study the non-Gaussianity of multiple-field inflation model using the method of the field equation. We start from reviewing the background and the perturbation theory of multiple-field inflation, and then derive the Klein-Gorden equation for the perturbations at second order. Afterward, we calculate the tree-level bispectrum of the fields’ perturbations and finally give the corresponding parameter fNL for the curvature perturbation ζ in virtue of the δN formalism. We also compare our result with the one already obtained from the Lagrangian formalism, and find they are consistent. This work may help us understand perturbation theory of inflation more deeply.