Consistency relation for cosmic magnetic fields

TL;DR

This paper derives a new consistency relation linking cosmic magnetic fields and scalar perturbations produced during inflation, offering a potential observational test for the primordial origin of cosmic magnetic fields.

Contribution

It introduces a simple consistency relation for the non-Gaussian cross correlation function in inflationary magnetogenesis models, aiding in testing previous calculations and probing the primordial nature of magnetic fields.

Findings

Derived a new consistency relation for the cross correlation in the squeezed limit.

Showed the relation's usefulness in testing existing models.

Proposed a novel observational probe of inflation through magnetic field correlations.

Abstract

If cosmic magnetic fields are indeed produced during inflation, they are likely to be correlated with the scalar metric perturbations that are responsible for the Cosmic Microwave Background anisotropies and Large Scale Structure. Within an archetypical model of inflationary magnetogenesis, we show that there exists a new simple consistency relation for the non-Gaussian cross correlation function of the scalar metric perturbation with two powers of the magnetic field in the squeezed limit where the momentum of the metric perturbation vanishes. We emphasize that such a consistency relation turns out to be extremely useful to test some recent calculations in the literature. Apart from primordial non-Gaussianity induced by the curvature perturbations, such a cross correlation might provide a new observational probe of inflation and can in principle reveal the primordial nature of cosmic magnetic fields.