Viable inflationary magnetogenesis with helical coupling

We consider helical coupling to electromagnetism and present a simple scenario of evolution of the coupling function leading to a viable inflationary magnetogenesis without the problem of back-reaction. In this scenario, helical magnetic fields of strength of order up to $10^{- 7}\,\text{G}$, when extrapolated to the current epoch, can be generated in a narrow spectral band centered at any reasonable wavenumber by adjusting the model parameters. We discuss implications of this model for baryogenesis, which impose additional constraints on the strength and correlation length of magnetic field.