Force-free electrodynamics is the theoretical paradigm used to describe electromagnetic fields in a region where the inertia of plasma is negligible compared to the strength of the electromagnetic field. While these fields are studied extensively around accreting black holes in an attempt to describe energy extraction, force-free fields also routinely appear in the study of cosmological magnetic fields. Despite this, there are no systematic studies of exact force-free fields in an expanding Universe. In this paper, we use geometric methods to find a wide variety of force-free solutions in a fixed Friedmann-Lemaître-Robertson-Walker metric background. The method we use can be directly generalized to any arbitrary electrically neutral spacetime, and hence provides a powerful tool to study force-free fields in general.

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• General relativity
• Primordial magnetic fields
• Relativistic aspects of cosmology