Helical cosmological magnetic fields from extra-dimensions

TL;DR

This paper explores the generation of helical cosmological magnetic fields during inflation within a higher-dimensional electromagnetic framework, showing that extra dimensions can produce observable magnetic fields consistent with current bounds.

Contribution

It introduces a higher-dimensional model with parity violation that naturally generates helical magnetic fields during inflation, providing analytical and numerical solutions for their evolution.

Findings

A scale-invariant spectrum of helical magnetic fields is achieved for D=4.

Generated magnetic fields can reach strengths of ~10^{-9} G.

The model complies with observational bounds from Planck and gamma-ray data.

Abstract

We study the inflationary generation of helical cosmological magnetic fields in a higher-dimensional generalization of the electromagnetic theory. For this purpose, we also include a parity breaking piece to the electromagnetic action. The evolution of extra-dimensional scale factor allows the breaking of conformal invariance of the effective electromagnetic action in $1+3$ dimensions required for such generation. Analytical solutions for the vector potential can be obtained in terms of Coulomb wave-functions for some special cases. We also present numerical solutions for the vector potential evolution in more general cases. In the presence of a higher-dimensional cosmological constant there exist solutions for the scale factors in which both normal and extra dimensional space either inflate or deflate simultaneously with the same rate. In such a scenario, with the number of extra dimensions $D=4$, a scale invariant spectrum of helical magnetic field is obtained. The net helicity arises, as one helical mode comes to dominate over the other at the superhorizon scales. A magnetic field strength of the order of $10^{-9}$ $G$ can be obtained for the inflationary scale $H\simeq 10^{-3}$ $M_{pl}$. Weaker fields will be generated for lower scales of inflation. Magnetic fields generated in this model respects the bounds on magnetic fields by Planck and $\gamma$-ray observations (i.e. $10^{-16}$ $G$ $<$ $B_{obs}<3.4\times 10^{-9}$ $G$).