Baryon asymmetry constraints on magnetic field from the Electroweak epoch

Decay of helical (hyper)magnetic fields that may have been present in the Universe during the Electroweak epoch can contribute to generation of the baryon asymmetry of the Universe. We revise constraints on the strength and correlation length of such fields from the requirement that their decay does not lead to over-production of the baryon asymmetry. We show that the helical fields with strength down to 1e-5 of the maximal possible strength during the Electroweak epoch should have had their correlation at least ~1e-6 of the Hubble radius during this epoch. For weaker fields this lower bound on the correlation length relaxes proportionally to the square of magnetic field strength. A field with parameters saturating the bound may actually be responsible for the baryon asymmetry observed today. We show that relic of such a field, surviving in the present day Universe in the form of intergalactic magnetic field detectable with Cherenkov Telescope Array Observatory, may have the strength up to 10-100 pG and can have parameters needed to affect the cosmological recombination and relax the Hubble tension. We also show that there is no constraint on the parameters of helical or non-helical magnetic fields stemming from the requirement that the baryon isocurvature perturbations produced by such fields during the Electroweak epoch are within the observational limits.