Baryon isocurvature constraints on the primordial hypermagnetic fields

It has been pointed out that hypermagnetic helicity decay at the electroweak symmetry breaking may have produced the observed baryon asymmetry of the Universe through the chiral anomaly in the standard model of particle physics. Although fully helical magnetic field that can adequately produce the observed baryon asymmetry is not strong enough to explain the origin of the intergalactic magnetic field inferred by the Fermi satellite, the mixture of helical and nonhelical primordial magnetic fields may explain both baryogenesis and the intergalactic magnetic fields simultaneously. We first show that such a scenario is ruled out by the constraint on the amplitude of baryon isocurvature perturbations produced by the primordial magnetic fields to avoid overproduction of deuterium at the big bang nucleosynthesis. Then we show that any attempt to explain the origin of intergalactic magnetic field by primordial magnetogenesis before the electroweak symmetry breaking does not work due to the above constraint irrespective of the helicity and baryogenesis mechanism.