Limit on primordial small-scale magnetic fields from cosmic microwave background distortions

Spatially varying primordial magnetic fields may be efficiently dissipated prior to the epoch of recombination due to the large viscosity of the baryon-photon fluid. We show that this dissipation may result in observable chemical potential and Compton y distortions in the cosmic microwave background spectrum. Current upper limits on and y from FIRAS constrain magnetic fields to have strength B0