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.

We study the physics potential of the detection of the Cosmic Neutrino Back- ground via neutrino capture on tritium, taking the proposed PTOLEMY experiment as a case study. With the projected energy resolution of ∆ ∼ 0.15eV, the experiment will be sensitive to neutrino masses with degenerate spectrum, m₁ ≃ m₂ ≃ m₃ = m_ν 0.1eV. These neutrinos are non-relativistic today; detecting them would be a unique opportunity to probe this unexplored kinematical regime. The signature of neutrino capture is a peak in the electron spectrum that is displaced by 2m_ν above the beta decay endpoint. The signal would exceed the background from beta decay if the energy resolution is ∆ 0.7 mν. Interestingly, the total capture rate depends on the origin of the neutrino mass, being Γ^D ≃ 4 and Γ^M ≃ 8 events per year (for a 100 g tritium target) for unclustered Dirac and Majorana neutrinos, respectively. An enhancement of the rate of up to O(1) is expected due to gravitational clustering, with the unique potential to probe the local overdensity of neutrinos. Turning to more exotic neutrino physics, PTOLEMY could be sensitive to a lepton asymmetry, and reveal the eV-scale sterile neutrino that is favored by short baseline oscillation searches. The experiment would also be sensitive to a neutrino lifetime on the order of the age of the uni- verse and break the degeneracy between neutrino mass and lifetime which affects existing bounds.