Enhancing the cross-correlations between magnetic fields and scalar perturbations through parity violation

TL;DR

This paper investigates how parity violation and helicity in magnetic fields during inflation enhance the cross-correlation with scalar perturbations, leading to stronger non-Gaussian signals, with implications for early universe cosmology.

Contribution

It introduces a numerical analysis of helical magnetic fields' cross-correlation with scalar perturbations, highlighting the amplification due to parity violation.

Findings

Helical magnetic fields significantly increase the non-Gaussianity parameter.

Parity violation enhances the amplitude of cross-correlations.

Hemispheric polarization modes are strongly amplified after Hubble exit.

Abstract

One often resorts to a non-minimal coupling of the electromagnetic field in order to generate magnetic fields during inflation. The coupling is expected to depend on a scalar field, possibly the same as the one driving inflation. At the level of three-point functions, such a coupling leads to a non-trivial cross-correlation between the perturbation in the scalar field and the magnetic field. This cross-correlation has been evaluated analytically earlier for the case of non-helical electromagnetic fields. In this work, we numerically compute the cross-correlation for helical magnetic fields. Non-Gaussianities are often generated as modes leave the Hubble radius. The helical electromagnetic modes evolve strongly (when compared to the non-helical case) around Hubble exit and one type of polarization is strongly amplified immediately after Hubble exit. We find that helicity considerably boosts the amplitude of the dimensionless non-Gaussianity parameter that characterizes the amplitude and shape of the cross-correlation between the perturbations in the scalar field and the magnetic field. We discuss the implications of the enhancement in the non-Gaussianity parameter due to parity violation.