Statistical anisotropy of the curvature perturbation from vector field perturbations.

@article{Dimopoulos2008StatisticalAO,
  title={Statistical anisotropy of the curvature perturbation from vector field perturbations.},
  author={Konstantinos Dimopoulos and Mindaugas Kar{\vc}iauskas and David H. Lyth and Yeinzon Rodriguez Department of Physics Lancaster University and Centro de Investigaciones Universidad Antonio Narino and Escuela de Fisica Universidad Industrial de Santander},
  journal={Journal of Cosmology and Astroparticle Physics},
  year={2008},
  volume={2009},
  pages={013-013}
}
The δN formula for the primordial curvature perturbation ζ is extended to include vector as well as scalar fields. Formulas for the tree-level contributions to the spectrum and bispectrum of ζ are given, exhibiting statistical anisotropy. The one-loop contribution to the spectrum of ζ 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 δN formula… 
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