Challenges in Inflationary Magnetogenesis: Constraints from Strong Coupling, Backreaction and the Schwinger Effect

摘要

Models of inflationary magnetogenesis with a coupling to the electromagneticaction of the form $f^2 F_{\mu\nu}F^{\mu\nu}$, are known to suffer from severalproblems. These include the strong coupling problem, the back reaction problemand also strong constraints due to Schwinger effect. We propose a model whichresolves all these issues. In our model, the coupling function, $f$, growsduring inflation and transits to a decaying phase post inflation. Thisevolutionary behaviour is chosen so as to avoid the problem of strong coupling.By assuming a suitable power law form of the coupling function, we can alsoneglect back reaction effects during inflation. To avoid back reactionpost-inflation, we find that the reheating temperature is restricted to bebelow $ \approx 1.7 \times 10^4$ GeV. The magnetic energy spectrum is predictedto be non-helical and generically blue. The estimated present day magneticfield strength and the corresponding coherence length taking reheating at theQCD epoch(150 MeV) are $ 1.4 \times 10^{-12}$ G and $6.1 \times 10^{-4}$ Mpc,respectively. This is obtained after taking account of nonlinear processingover and above the flux freezing evolution after reheating. If we consider alsothe possibility of a non-helical inverse cascade, as indicated in directnumerical simulations, the coherence length and the magnetic field strength areeven larger. In all cases mentioned above, the magnetic fields generated in ourmodels satisfy the $\gamma$-ray bound below a certain reheating temperature.