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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, $n(t_0) < 1 \times 10^{-20}~{\rm cm}^{-3}$, 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 $φ{\bf E}\cdot {\bf B}$ 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. 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 using the suggested strength $\sim 10^{-14}~{\rm G}$ and coherence length $\sim 10~{\rm Mpc}$ we find $μ_ν\lesssim 10^{-16} μ_B$.