On the non-Gaussian correlation of the primordial curvature perturbation with vector fields

TL;DR

This paper calculates the non-Gaussian three-point correlation between primordial curvature perturbations and vector fields during inflation, highlighting potential signatures of primordial magnetic fields with significant non-Gaussianity.

Contribution

It provides the first detailed computation of the three-point cross-correlation involving curvature perturbation and vector fields in models with broken conformal invariance during inflation.

Findings

Maximum non-Gaussian signal at flattened configuration with |b_{NL}| ~ 10^3

Results consistent with magnetic consistency relation in the squeezed limit

Potential observational signatures of primordial magnetic fields

Abstract

We compute the three-point cross-correlation function of the primordial curvature perturbation generated during inflation with two powers of a vector field in a model where conformal invariance is broken by a direct coupling of the vector field with the inflaton. If the vector field is identified with the electromagnetic field, this correlation would be a non-Gaussian signature of primordial magnetic fields generated during inflation. We find that the signal is maximized for the flattened configuration where the wave number of the curvature perturbation is twice that of the vector field and in this limit, the magnetic non-linear parameter becomes as large as |b_{NL}| ~ 10^3. In the squeezed limit where the wave number of the curvature perturbation vanishes, our results agree with the magnetic consistency relation derived in arXiv:1207.4187.