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The \delta N formula for the primordial curvature perturbation \zeta isextended to include vector as well as scalar fields. Formulas for thetree-level contributions to the spectrum and bispectrum of \zeta are given,exhibiting statistical anisotropy. The one-loop contribution to the spectrum of\zeta is also worked out. We then consider the generation of vector fieldperturbations from the vacuum, including the longitudinal component that willbe present if there is no gauge invariance. Finally, the \delta N formula isapplied to the vector curvaton and vector inflation models with the tensorperturbation also evaluated in the latter case.

Statistical anisotropy of the curvature perturbation from vector field perturbations