The magnetic origin of primordial black holes: a viable dark matter scenario

Abstract The origin of primordial magnetic fields and the nature of dark matter remain open problems in cosmology, largely due to the absence of direct observational probes of early-Universe magnetogenesis. Primordial black holes (PBHs) provide a potential link between these two issues, as their formation is sensitive to small-scale energy-density fluctuations. In this work, we investigate PBH formation sourced by primordial magnetic fields generated in the early Universe. We consider a magnetogenesis scenario that can account for the observed large-scale magnetic fields while also allowing PBH formation in a mass range consistent with PBHs constituting a significant fraction of the cold dark matter. We further analyze the stochastic gravitational-wave background produced by magnetic-field-induced anisotropic stresses and show that, for certain regions of parameter space, the resulting signal lies within the projected sensitivity of future gravitational-wave observatories such as LISA, DECIGO, BBO, and SKA. By comparing the parameter dependence of the PBH abundance and the gravitational-wave spectrum, we demonstrate that these observables provide complementary constraints on the underlying magnetogenesis model. Our results illustrate how combining PBH and gravitational-wave observations can improve our ability to test magnetogenesis scenarios and probe early-Universe dynamics.