Viscous damping of chiral dynamos in the early universe

Chiral dynamo converting asymmetry between right and left-handed leptons in the early universe into helical magnetic field has been proposed as a possible cosmological magnetogenesis scenario. We show that this mechanism is strongly affected by viscous damping of primordial plasma motions excited by the dynamo. This effect modifies the expected range of strength and correlation length of the chiral dynamo field which could have survived till present epoch in the voids of the Large Scale Structure. We show the range of parameters of chiral dynamo field that may have survived in the voids is still consistent with existing lower bounds on intergalactic magnetic field from gamma-ray observations, but only if the right-left lepton asymmetry at the temperature T~80 TeV is very high, close to the maximal possible value.