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 } { 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 g _ { a \gamma } \varphi { \bf E } \cdot { \bf B } / 4 \pi 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 ( CMB ) photons into axions lead to g _ { a \gamma } \lesssim 10 ^ { -9 } ~ { } { GeV } ^ { -1 } for the suggested PMF strength \sim 10 ^ { -14 } { G } and coherence length \sim 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 \mu _ { \nu } \lesssim 10 ^ { -16 } \mu _ { B } .