We study baryon asymmetry generation originated from the leptogenesis in the presence of hypermagnetic fields in the early Universe plasma before the electroweak phase transition ( EWPT ) .
For the simplest Chern-Simons ( CS ) wave configuration of hypermagnetic field we find the baryon asymmetry growth when the hypermagnetic field value changes due to \alpha ^ { 2 } -dynamo and the lepton asymmetry rises due to the Abelian anomaly .
We solve the corresponding integro-differential equations for the lepton asymmetries describing such self-consistent dynamics for lepto- and baryogenesis in the two scenarios : ( i ) when a primordial lepton asymmetry sits in right electrons e _ { R } ; and ( ii ) when , in addition to e _ { R } , a left lepton asymmetry for e _ { L } and \nu _ { eL } arises due to chirality flip reactions provided by inverse Higgs decays at the temperatures , T < T _ { \mathrm { RL } } \sim 10 \thinspace \text { TeV } .
We find that the baryon asymmetry of the Universe ( BAU ) rises very fast through such leptogenesis , especially , in strong hypermagnetic fields .
Varying ( decreasing ) the CS wave number parameter k _ { 0 } < 10 ^ { -7 } T _ { \mathrm { EW } } one can recover the observable value of BAU , \eta _ { \mathrm { B } } \sim 10 ^ { -9 } , where k _ { 0 } = 10 ^ { -7 } T _ { \mathrm { EW } } corresponds to the maximum value for CS wave number surviving ohmic dissipation of hypermagnetic field .
In the scenario ( ii ) one predicts the essential difference of the lepton numbers of right - and left electrons at EWPT time , L _ { eR } - L _ { eL } \sim ( \mu _ { eR } - \mu _ { eL } ) / T _ { \mathrm { EW } } = \Delta \mu / T _ { \mathrm { EW } } % \simeq 10 ^ { -5 } that can be used as an initial condition for chiral asymmetry after EWPT .