Résumé
Magnetic fields appear to be present in essentially all astrophysical environments, including galaxies, clusters of galaxies and voids. There are both observational and theoretical motives for considering the possibility of their origin tracing back to the events in the very early universe, such as the electroweak phase transition or Inflation. Such a primordial magnetic field (PMF) would remain embedded in the plasma and evolve to persist through the radiation and matter eras, and to the present day. As described in this Chapter, a PMF present in the primordial plasma prior to recombination could help relieve the Hubble tension. A stochastic magnetic field would induce inhomogeneities, pushing the baryons into regions of lower magnetic energy density and speeding up the recombination process. As a consequence, the sound horizon at last scattering would be smaller, which is a necessary ingredient for relieving the Hubble tension. Intriguingly, the strength of the magnetic field required to alleviate the tension is of the right order to also explain the observed magnetic fields in galaxies, clusters of galaxies and voids. These findings motivate further detailed studies of recombination in the presence of PMFs and observational tests of this hypothesis.