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

Understand

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 $f_{NL}$ for the curvature perturbation $\zeta$ in virtue of the $\delta N$ formalism.
• We also compare our result with the one already obtained from the Lagrangian formalism, and find they are consistent.