Statistical anisotropy of the curvature perturbation from vector field perturbations

Understand

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.