On inflating magnetic fields, and the backreactions thereof

We investigate in more depth the issue of backreaction in models that attempt at generating cosmological magnetic fields at inflation. By choosing different, physically motivated, parametrisations, we are able to isolate the core of the problem, namely the existence, alongside the wanted magnetic field, of its electric counterpart, which turns out quite generally to be stronger and redder. We were also able to identify a few more interwoven weak spots (the typically very high scale of inflation, the width of the spectrum of modes processed by inflation, the blindness of the amplification mechanism to the energy scale processed), in a way independent on the specifications of the coupling between inflation and electromagnetism. Despite having stripped down the problem to the core, the obstacles encountered appear insurmountable, thereby posing a challenge to inflation as the incubator of cosmological magnetism.