Implications of a Primordial Magnetic Field for Magnetic Monopoles, Axions, and Dirac Neutrinos

We explore some particle physics implications of the growing evidence for a helical primordial magnetic field (PMF). From the interactions of magnetic monopoles and the PMF, we derive an upper bound on the monopole number density, nðt0Þ < 1 × 10−20 cm−3, which is a “primordial” analog of the Parker bound for the survival of galactic magnetic fields. Our bound is weaker than existing constraints, but it is derived under independent assumptions. We also show how improved measurements of the PMF at different redshifts can lead to further constraints on magnetic monopoles. Axions interact with the PMF due to the gaγφE · B=4π interaction. Including the effects of the cosmological plasma, we find that the helicity of the PMF is a source for the axion field. Although the magnitude of the source is small for the PMF, it could potentially be of interest in astrophysical environments. Earlier derived constraints from the resonant conversion of cosmic microwave background photons into axions lead to gaγ ≲ 10−9 GeV−1 for the suggested PMF strength ∼10−14 G and coherence length ∼10 Mpc. Finally, we apply constraints on the neutrino magnetic dipole moment that arise from requiring successful big bang nucleosynthesis in the presence of a PMF, and we find μν ≲ 10−16 μB.