Magnetic fields from inflation: the transition to the radiation era

TL;DR

This work investigates how primordial magnetic fields generated during inflation, via a conformal-invariance-violating coupling $f^2(\varphi)F^{\mu\nu}F_{\mu\nu}$, source scalar metric perturbations and influence the subsequent radiation era. By solving the Bardeen equation with a magnetic-field source on superhorizon scales and performing a careful matching across the inflation-to-radiation transition, the authors show that the leading inflationary magnetic mode $\propto (k\eta)^{-2}$ transfers to a decaying mode in the radiation era, while a new, constant-mode perturbation proportional to the end-of-inflation curvature perturbation $\zeta_*$ survives. This constant mode adds to the usual passive and compensated contributions and can be enhanced, particularly for scale-invariant spectra, by logarithmic factors, potentially elevating the CMB signal from inflationary magnetic seeds and introducing non-Gaussian features. The results imply that inflationary magnetogenesis could yield observable imprints in the CMB and large-scale structure, offering a pathway to probe primordial magnetic fields down to very small strengths, albeit with caveats related to gauge symmetry and model-specific details.

Abstract

We compute the contribution to the scalar metric perturbations from large-scale magnetic fields which are generated during inflation. We show that apart from the usual passive and compensated modes, the magnetic fields also contribute to the constant mode from inflation. This is different from the causal (post inflationary) generation of magnetic fields where such a mode is absent and it might lead to significant, non-Gaussian CMB anisotropies.