Suppressed Magnetogenesis from Ultralight Dark Matter due to Finite Conductivity

Recently, a mechanism for generating astrophysically relevant magnetic fields via ultralight pseudoscalar dark matter, through the coupling term $g_{\phi \gamma} \phi F_{\mu \nu}\tilde{F}^{\mu\nu}$ in the Lagrangian density, was proposed in Brandenberger et al (2026) (see Ref. 1). In this scenario, the electromagnetic fields are amplified through the phenomena of parametric resonance due to the oscillatory behaviour of the pseudoscalar field. However, the analysis presented in that work does not account for the effects of a conducting medium. In this paper, we incorporate the finite conductivity of the plasma into the dynamics of the pseudoscalar and electromagnetic fields. We show that, due to the large conductivity relative to the Hubble parameter, the amplification of the electromagnetic fields due to parametric resonance is significantly suppressed. Consequently, we find that, for observationally viable values of the coupling between the electromagnetic field and the ultralight pseudoscalar field, it is not possible to generate magnetic fields of sufficient strength to explain their presence in cosmic voids.