Primordial black holes from vector-induced curvature perturbations sourced by primordial magnetic fields

Generating an appreciable abundance of primordial black holes (PBHs) requires a substantial enhancement of primordial curvature perturbations on small scales. In this work, we propose a new post-inflationary mechanism in which such an enhancement arises during a stiff, or kination, epoch. The mechanism is driven by metric vector perturbations sourced by the vector component of the electromagnetic stress-energy tensor associated with primordial magnetic fields (PMFs). Since these first-order vector modes remain approximately constant during kination, they act as persistent nonlinear sources for second-order scalar perturbations. We show that the resulting vector-induced curvature perturbations are amplified toward the infrared cutoff of the kination band and exhibit the characteristic scaling $\mathcal P_{\mathcal R}(k)\propto k^{-5}$. As a concrete realization, we consider PMFs generated in a Ratra-type magnetogenesis scenario and find that the induced curvature perturbations can produce PBHs with an abundance large enough to constitute a substantial fraction of the dark matter.