Non-gaussianity of inflationary field perturbations from the field equation

We calculate the tree-level bispectrum of the inflaton field perturbation directly from the field equations, and construct the corresponding f_NL parameter. Our results agree with previous ones derived from the Lagrangian. We argue that quantum theory should only be used to calculate the correlators when they first become classical a few Hubble times after horizon exit, the classical evolution taking over thereafter.Comment: 16 pages, uses iopart.sty. v2: replaced with version accepted by JCAP; minor changes of wording only. v3: supersedes version published by journal; typo fixed in Eq. (20) and updated references. v4: sign errors in Eqs. (32) and (38) correcte