Effective treatment of U(1) gauge field and charged particles in axion
  inflation
  The axionic inflaton with the Chern-Simons coupling may generate U(1) gauge
fields and charged particles simultaneously. In order to incorporate the
backreaction from the charged particles on the gauge fields, we develop a
procedure to obtain an equilibrium solution for the gauge fields by treating
the induced current as effective electric and magnetic conductivities.
Introducing mean field approximation, and numerically solving self-consistency
equations, we find that the gauge field amplitudes are drastically suppressed.
Interestingly, as the production becomes more efficient, the charged particles
gain a larger part of the transferred energy from the inflaton and eventually
dominate it. Our formalism offers a basis to connect this class of inflationary
models to a rich phenomenology such as baryogenesis and magnetogenesis.
