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

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.

v1: 20 pages, 4 figures; v2: 20 pages, 4 figures, references added; v3: 20 pages, 4 figures, minor changes, version published in JCAP. arXiv admin note: text overlap with arXiv:1807.05530