Models of inflationary magnetogenesis with a coupling to the electromagnetic action of the form f ^ { 2 } F _ { \mu \nu } F ^ { \mu \nu } , are known to suffer from several problems .
These include the strong coupling problem , the back reaction problem and also strong constraints due to 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 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 also neglect back reaction effects during inflation .
To avoid back reaction post-inflation , we find that the reheating temperature is restricted to be below \approx 1.7 \times 10 ^ { 4 } GeV .
The magnetic energy spectrum is predicted to be non-helical 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 \times 10 ^ { -12 } G and 6.1 \times 10 ^ { -4 } 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 non-helical 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 \gamma -ray bound below a certain reheating temperature .