Magnetogenesis with gravitational waves and primordial black hole dark matter

Strongly supercooled first order phase transitions (FOPTs) can produce primordial black hole (PBH) dark matter (DM) along with observable gravitational waves (GWs) from bubble collisions. Such FOPTs may also produce coherent magnetic fields generated by bubble collisions and by turbulence in the primordial plasma. Here we find that the requirement for PBH DM can produce large primordial magnetic fields which subsequently yield intergalactic magnetic fields in the present universe (with magnitude $\lesssim 20$ pG across coherence length scales of $\simeq 0.001$-$0.01$ Mpc, assuming maximally helical magnetic fields) that easily exceed lower bounds from blazar observations. We follow a largely model independent approach and highlight the possibility of producing DM and observable multi-messenger magnetic fields and GW signals visible in next generation experiments.