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If the B-mode signal in the CMB polarization seen by the BICEP2 experiment isconfirmed, it has dramatic implications for models of inflation. The result isalso in tension with Planck limits on standard inflationary models. It istherefore important to investigate whether this signal can arise fromalternative sources. If so, this could lessen the pressure on inflationarymodels and the tension with Planck data. We investigate whether vector andtensor modes from primordial magnetic fields can explain the signal. We findthat in principle, magnetic fields generated during inflation can indeedproduce the required B-mode, for a suitable range of energy scales ofinflation. In this case, the primordial gravitational wave amplitude isnegligible, so that there is no tension with Planck and no problems posed forcurrent inflationary models. However, the simplest magnetic model is in tensionwith Planck limits on non-Gaussianity in the trispectrum. It may be possible tofine-tune the magnetogenesis model so that this non-Gaussianity is suppressed.Alternatively, a weaker magnetic field can pass the non-Gaussianity constraintsand allow the primordial tensor mode to be reduced to r~0.09, thus removing thetension with Planck data and alleviating the problems with simple inflationarymodels.

Can primordial magnetic fields be the origin of the BICEP2 data?