CMB spectral distortions from the decay of causally generated magnetic
  fields
  We improve previous calculations of the CMB spectral distortions due to the
decay of primordial magnetic fields. We focus our studies on causally generated
magnetic fields at the electroweak and QCD phase transitions. We also consider
the decay of helical magnetic fields. We show that the decay of non-helical
magnetic fields generated at either the electroweak or QCD scale produce $\mu$
and $y$-type distortions below $10^{-8}$ which are probably not detectable by a
future PIXIE-like experiment. We show that magnetic fields generated at the
electroweak scale must have a helicity fraction $f_*>10^{-4}$ in order to
produce detectable $\mu$-type distortions. Hence a positive detection coming
from the decay of magnetic fields would rule out non-helical primordial
magnetic fields and provide a lower bound on the magnetic helicity.
