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 U(1)^ 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 10⁴ GeV and 10¹¹ 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 10¹¹ GeV can be correlated with Hawking evaporation signals at future gamma-ray telescopes. LISA can probe the entire range of PBH masses between 1× 10⁻¹⁶M_ and 8× 10⁻¹¹M_ if PBHs fully account for the dark matter abundance. For Z' masses between 40 TeV and 10⁴ TeV, and 10 TeV right-handed neutrinos, helical magnetic fields can be produced with magnitudes 0.5 pG and coherence lengths 0.008 Mpc, above current blazar lower bounds.