Inflationary dynamics of kinetically-coupled gauge fields

We investigate the inflationary dynamics of two kinetically-coupled massless $U(1)$ gauge fields with time-varying kinetic-term coefficients. Ensuring that the system does not have strongly coupled regimes shrinks the parameter space. Also, we further restrict ourselves to systems that can be quantized using the standard creation, annihilation operator algebra. This second constraint limits us to scenarios where the system can be diagonalized into the sum of two decoupled, massless, vector fields with a varying kinetic-term coefficient. Such a system might be interesting for magnetogenesis because of how the strong coupling problem generalizes. We explore this idea by assuming that one of the gauge fields is the Standard Model $U(1)$ field and that the other dark gauge field has no particles charged under its gauge group. We consider whether it would be possible to transfer a magnetic field from the dark sector, generated perhaps before the coupling was turned on, to the visible sector. We also investigate whether the simple existence of the mixing provides more opportunities to generate magnetic fields. We find that neither possibility works efficiently, consistent with the well-known difficulties in inflationary magnetogenesis.