Gauge Field and Fermion Production during Axion Inflation
  We study the dual production of helical Abelian gauge fields and chiral
fermions through the Chern-Simons (CS) coupling with a pseudo-scalar inflaton
in the presence of a chiral anomaly. Through the CS term, the motion of the
inflaton induces a tachyonic instability for one of the two helicities of the
gauge field. We show that the resulting helical gauge field necessarily leads
to the production of chiral fermions by deforming their Fermi sphere into
discrete Landau levels. The population of the lowest Landau level leads to a
chiral asymmetry as inferred from the chiral anomaly, while the higher levels
are populated symmetrically through pair production. From the backreaction of
the fermions on the gauge field production we derive a conservative but
stringent upper bound on the magnitude of the gauge fields. Consequently, we
find that the scalar perturbations sourced by these helical gauge fields,
responsible for enhanced structure formation on small scales, get reduced
significantly. We also discuss the fate of the primordial chiral asymmetry and
of the helical gauge fields after inflation, and show that the instability in
the chiral plasma tends to erase these primordial asymmetries. This result may
impact scenarios where the baryon asymmetry of the Universe is connected to
primordial magnetic fields.
