Statistical anisotropy of the curvature perturbation from vector field perturbations

TL;DR

This paper extends the N formalism to include vector fields, analyzing their contributions to primordial curvature perturbations and demonstrating resulting statistical anisotropy in the spectrum and bispectrum.

Contribution

It introduces formulas for vector field contributions to N, including one-loop effects and applications to vector curvaton and inflation models.

Findings

Vector fields induce statistical anisotropy in curvature perturbations.

The extended N formalism accounts for vector perturbations and their observational signatures.

Applications to vector curvaton and inflation models show significant effects.

Abstract

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.