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

TL;DR

This paper investigates how a gauge field coupled to the inflaton can produce statistically anisotropic curvature perturbations during inflation, providing a simplified calculation and discussing implications for the origin of the curvature perturbation.

Contribution

It offers a simpler, more complete classical calculation of anisotropic curvature perturbations from gauge fields coupled to the inflaton, expanding understanding of their observational signatures.

Findings

Gauge field perturbations can generate observable anisotropic curvature perturbations.

The entire curvature perturbation may be produced during inflation or afterwards.

The classical approach confirms previous quantum in-in formalism results.

Abstract

The inflaton might be coupled to a gauge field through a term f^2(\phi) F_\mu\nu F^\mu\nu. If f \propto a^{-2} where a(t) is the scale factor, the perturbation \delta W 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 \zeta (both the statistically isotropic and anisotropic parts) is generated during slow-roll inflation, or else it is generated afterwards.