Can primordial magnetic fields be the origin of the BICEP2 data?
  If the B-mode signal in the CMB polarization seen by the BICEP2 experiment is
confirmed, it has dramatic implications for models of inflation. The result is
also in tension with Planck limits on standard inflationary models. It is
therefore important to investigate whether this signal can arise from
alternative sources. If so, this could lessen the pressure on inflationary
models and the tension with Planck data. We investigate whether vector and
tensor modes from primordial magnetic fields can explain the signal. We find
that in principle, magnetic fields generated during inflation can indeed
produce the required B-mode, for a suitable range of energy scales of
inflation. In this case, the primordial gravitational wave amplitude is
negligible, so that there is no tension with Planck and no problems posed for
current inflationary models. However, the simplest magnetic model is in tension
with Planck limits on non-Gaussianity in the trispectrum. It may be possible to
fine-tune the magnetogenesis model so that this non-Gaussianity is suppressed.
Alternatively, a weaker magnetic field can pass the non-Gaussianity constraints
and allow the primordial tensor mode to be reduced to r~0.09, thus removing the
tension with Planck data and alleviating the problems with simple inflationary
models.
