  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.
