Primordial Helical Magnetic Fields from Inflation?
  We revisit the mechanism of helical magnetogenesis during inflation with a
parity violating interaction using the formalism of stochastic inflation. One
of the polarization of the gauge field undergoes tachyonic growth leading to
the generation of helical magnetic fields. We obtain the Langevin equations
associated with the electromagnetic fields which are in the form of
Ornstein-Uhlenbeck stochastic differential equations. Consequently, the
tachyonic growth of the helical magnetic fields is balanced by a mean-reverting
process of stochastic dynamics such that the magnetic fields settle down to an
equilibrium state with the amplitude smaller than what is obtained in the
absence of the stochastic noises. Working in the parameter space of the model
where both the backreaction and the strong coupling problems are under control
the model does not provide large enough seed to be amplified by the galactic
dynamo as the source of the magnetic fields observed on cosmological scales.
