Vacuum polarization and photon mass in inflation

We give a pedagogical review of a mechanism through which long wave length photons can become massive during inflation. Our account begins with a discussion of the period of exponentially rapid expansion known as inflation. We next describe how, when the universe is not expanding, quantum fluctuations in charged particle fields cause even empty space to behave as a polarizable medium. This is the routinely observed phenomenon of vacuum polarization. We show that the quantum fluctuations of low mass, scalar fields are enormously amplified during inflation. If one of these fields is charged, the vacuum polarization effect of flat space is strengthened to the point that long wave length photons acquire mass. Our result for this mass is shown to agree with a simple model in which the massive photon electrodynamics of Proca emerges from applying the Hartree approximation to scalar quantum electrodynamics during inflation. A huge photon mass is not measured today because the original phase of inflation ended when the universe was only a tiny fraction of a second old. However, the zero-point energy left over from the epoch of large photon mass may have persisted during the post-inflationary universe as very weak, but cosmological-scale, magnetic fields. It has been suggested that these small seed fields were amplified by a dynamo mechanism to produce the micro-Gauss magnetic fields observed in galaxies and galactic clusters.