It has been found that long range magnetic fields in microgauss range exists at distance of about 5 billion light years (see this).
The presence of cosmic magnetic fields is one of the mysteries challenging not only the existing cosmological models but even the standard model itself. Due to high temperatures there are no long range currents and there should be no long range magnetic fields in early cosmology and also the mechanism for their emergence later has remained mystery.
The observations, in particular the observations described in the article, are in conflict with the standard model view. The TGD explanation is direct implication of the assumption space-time is surface in M4×CP2. CP2 has non-trivial homology: one can regard it as having 4-D space with Euclidian signature of metric and carrying as topological magnetic monopole flux. No magnetic charge but non-trivial magnetic flux over homologically non-trivial 2-surfaces.
At space-time level this implies the existence of cosmic strings carrying monopole flux and having huge magnetic energy per unit length: they are essentially objects with 2-D M4 projection obeying string dynamics (minimal surface) and having 2-D complex surface as CP2 projection. No currents are needed to create these magnetic fields and they are stable for purely topological reasons. The very early universe would consist of a gas or plasma like state of cosmic strings.
After that the TGD analog of inflationary period took place and the projections M4 of flux tubes became 4-D. Cosmic strings started to thicken and magnetic fields gradually weakened. The prediction that magnetic fields were strongest in the early universe conforms with the observations. Standard model predicts just the opposite and cannot even provide a plausible mechanism for how they could have got stronger.
Other predictions are a detailed model for galactic dark matter associated with thickening cosmic strings. No dark matter halo is predicted and automatically correct prediction for the velocity spectrum of distant stars follows.
See the the chapter Breaking of CP, P, and T in cosmological scales in TGD Universe .