A variety of observations impose upper limits at the nano Gauss level on magnetic fields that are coherent on inter-galactic scales while blazar observations indicate a lower bound $sim 10^{-16}$ Gauss. Such magnetic fields can play an important astrophysical role, for example at cosmic recombination and during structure formation, and also provide crucial information for particle physics in the early universe. Magnetic fields with significant energy density could have been produced at the electroweak phase transition. The evolution and survival of magnetic fields produced on sub-horizon scales in the early universe, however, depends on the magnetic helicity which is related to violation of symmetries in fundamental particle interactions. The generation of magnetic helicity requires new CP violating interactions that can be tested by accelerator experiments via decay channels of the Higgs particle.
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