Statistical anisotropy of the curvature perturbation from vector field perturbations

The delta N formula for the primordial curvature perturbation zeta is extended to include vector as well as scalar fields. Formulas for the tree-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 field perturbations from the vacuum, including the longitudinal component that will be present if there is no gauge invariance. Finally, the delta N formula is applied to the vector curvaton and vector inflation models with the tensor perturbation also evaluated in the latter case.