Primordial magnetic fields from metric perturbations

Abstract

We study the amplification of electromagnetic vacuum fluctuations induced by the evolution of scalar metric perturbations at the end of inflation. Such perturbations break the conformal invariance of Maxwell equations in Friedmann-Robertson-Walker backgrounds and allow the growth of magnetic fields on super-Hubble scales. We relate the strength of the fields generated by this mechanism with the power spectrum of scalar perturbations and estimate the amplification on galactic scales for different values of the spectral index. Finally we discuss the possible effects of finite conductivity during reheating.