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.

Cosmic strings can arise in hidden sector models with a spontaneously broken Abelian symmetry group. We have studied the couplings of the Standard Model fields to these so-called dark strings in the companion paper. Here we survey the cosmological and astrophysical observables that could be associated with the presence of dark strings in our universe with an emphasis on low-scale models, perhaps TeV . Specifically, we consider constraints from nucleosynthesis and CMB spectral distortions, and we calculate the predicted fluxes of diffuse gamma ray cascade photons and cosmic rays. For strings as light as TeV, we find that the predicted level of these signatures is well below the sensitivity of the current experiments, and therefore low scale cosmic strings in hidden sectors remain unconstrained. Heavier strings with a mass scale in the range 10¹³ GeV to 10¹⁵ GeV are at tension with nucleosynthesis constraints.

The existence of a cosmological magnetic field could be revealed by the effects of non-trivial helicity on large scales. We evaluate a CP (conjugation plus parity) odd statistic, Q, using gamma-ray data obtained from Fermi satellite observations at high galactic latitudes to search for such a signature. Observed values of Q are found to be non-zero; the probability of a similar signal in Monte Carlo simulations is ∼0.2 per cent. Contamination from the Milky Way does not seem to be responsible for the signal since it is present even for data at very high galactic latitudes. Assuming that the signal is indeed due to a helical cosmological magnetic field, our results indicate left-handed magnetic helicity and field strength ∼10^-14 G on ∼10 Mpc scales.