Primordial black holes and magnetic fields in conformal neutrino mass models

Sufficiently strong and long-lasting first-order phase transitions can produce primordial black holes (PBHs) that contribute substantially to the dark matter abundance of the Universe, and can produce large-scale primordial magnetic fields. We study these mechanisms in a generic class of conformal $\mathrm{U(1)}^\prime$ models that also explain active neutrino oscillation data via the type-I seesaw mechanism. We find that phase transitions that occur at seesaw scales between $10^4$ GeV and $10^{11}$ GeV produce gravitational wave signals (from the dynamics of the phase transition and from the decay of cosmic string loops) at LISA/ET that can be correlated with microlensing signals of PBHs at the Roman Space Telescope, while scales near $10^{11}$ GeV can be correlated with Hawking evaporation signals at future gamma-ray telescopes. LISA can probe the entire range of PBH masses between $1\times 10^{-16}M_\odot$ and $8\times 10^{-11}M_\odot$ if PBHs fully account for the dark matter abundance. For Z' masses between 40 TeV and $10^4$ TeV, and 10 TeV right-handed neutrinos, helical magnetic fields can be produced with magnitudes $\gtrsim 0.5$ pG and coherence lengths $\gtrsim 0.008$ Mpc, above current blazar lower bounds.