Challenges in inflationary magnetogenesis: Constraints from strong coupling, backreaction, and the Schwinger effect

Abstract

Models of inflationary magnetogenesis with a coupling to the electromagnetic action of the form ${f}^{2}{F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}$, are known to suffer from several problems. These include the strong coupling problem, the backreaction problem and also strong constraints due to the Schwinger effect. We propose a model which resolves all these issues. In our model, the coupling function, $f$, grows during inflation and transits to a decaying phase post-inflation. This evolutionary behavior is chosen so as to avoid the problem of strong coupling. By assuming a suitable power-law form of the coupling function, we can also neglect backreaction effects during inflation. To avoid backreaction post-inflation, we find that the reheating temperature is restricted to be below $\ensuremath{\approx}1.7\ifmmode\times\else\texttimes\fi{}{10}^{4}\text{ }\text{ }\mathrm{GeV}$. The magnetic energy spectrum is predicted to be nonhelical and generically blue. The estimated present day magnetic field strength and the corresponding coherence length taking reheating at the QCD epoch (150 MeV) are $1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{G}$ and $6.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }\text{ }\mathrm{Mpc}$, respectively. This is obtained after taking account of nonlinear processing over and above the flux-freezing evolution after reheating. If we consider also the possibility of a nonhelical inverse transfer, as indicated in direct numerical simulations, the coherence length and the magnetic field strength are even larger. In all cases mentioned above, the magnetic fields generated in our models satisfy the $\ensuremath{\gamma}$-ray bound below a certain reheating temperature.