Paper detail

The statistically anisotropic curvature perturbation generated by f(ϕ)^2 F^2

The inflaton might be coupled to a gauge field through a term f^2(ϕ) F_μνF^μν. If f \propto a^{-2} where a(t) is the scale factor, the perturbation δW of the gauge field generates a potentially observable statistically anisotropic contribution to the primordial curvature perturbation during slow-roll inflation. The spectrum and bispectrum of this contribution have been calculated using the in-in formalism of quantum field theory. We give a simpler and more complete calculation using only the classical perturbations. The results suggest that either the entire curvature perturbation ζ(both the statistically isotropic and anisotropic parts) is generated during slow-roll inflation, or else it is generated afterwards.