Magnetic Fields from Compensated Isocurvature Perturbations

Compensated isocurvature perturbations (CIPs) are perturbations to the primordial baryon density that are accompanied by dark-matter-density perturbations so that the total matter density is unperturbed. Such CIPs, which may arise in some multi-field inflationary models, can be long-lived and only weakly constrained by current cosmological measurements. Here we show that the CIP-induced modulation of the electron number density interacts with the electron-temperature fluctuation associated with primordial adiabatic perturbations to produce, via the Biermann-battery mechanism, a magnetic field in the post-recombinaton Universe. Assuming the CIP amplitude saturates the current BBN bounds, this magnetic field can be stronger than ${10}^{-15}\mathrm{n}\mathrm{G}$ at $z\simeq 20$ and stronger by an order of magnitude than that (produced at second order in the adiabatic-perturbation amplitude) in the standard cosmological model, and thus can serve as a possible seed for galactic dynamos.