The statistically anisotropic curvature perturbation generated by f2(φ)FμνFμν

The inflaton might be coupled to a gauge field through a term f2(φ)FμνFμν. If f∝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