Axion driven cosmic magneto-genesis during the QCD crossover
  We propose a mechanism for the generation of a magnetic field in the early
universe during the QCD crossover assuming that dark matter is made of axions.
Thermoelectric fields arise at pressure gradients in the primordial plasma due
to the difference in charge, energy density and equation of state between the
quark and lepton components. The axion field is coupled to the EM field, so
when its spatial gradient is misaligned with the thermoelectric field, an
electric current is driven. Due to the finite resistivity of the plasma an
electric field appears that is generally rotational. For a QCD axion mass
consistent with observational constraints and a conventional efficiency for
turbulent dynamo amplification --- driven by the same pressure gradients
responsible for the thermoelectric fields --- a magnetic field is generated on
subhorizon scales. After significant Alfv\'enic unwinding it reaches a present
day strength of $B \sim 10^{-13 }$ G on a characteristic scale $L_B \sim $ 20
pc. The resulting combination of $BL_B^{1/2}$ is significantly stronger than in
any astrophysical scenario, providing a clear test for the cosmological origin
of the field through $\gamma$-ray observations of distant blazars. The
amplitude of the pressure gradients may be inferred from the detection of
concomitant gravitational waves, while several experiments are underway to
confirm or rule out the existence of axions.
