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.
