Inflationary Magnetogenesis without the Strong Coupling Problem

The simplest gauge invariant models of inflationary magnetogenesis are known to suffer from the problems of either large backreaction or strong coupling, which make it difficult to self-consistently achieve cosmic magnetic fields from inflation with a field strength larger than $10^{-32} G$ today on the $\Mpc$ scale. Such a strength is insufficient to act as seed for the galactic dynamo effect, which requires a magnetic field larger than $10^{-20} G$. In this paper we analyze simple extensions of the minimal model, which avoid both the strong coupling and back reaction problems, in order to generate sufficiently large magnetic fields on the Mpc scale today. First we study the possibility that the coupling function which breaks the conformal invariance of electromagnetism is non-monotonic with sharp features. Subsequently, we consider the effect of lowering the energy scale of inflation jointly with a scenario of prolonged reheating where the universe is dominated by a stiff fluid for a short period after inflation. In the latter case, a systematic study shows upper bounds for the magnetic field strength today on the Mpc scale of $10^{-13} G$ for low scale inflation and $10^{-25} G$ for high scale inflation, thus improving on the previous result by 7-19 orders of magnitude. These results are consistent with the strong coupling and back reaction constraints.