Chiral plasma instability in the early Universe and its implications on baryogenesis

In the presence of the chiral asymmetry and magnetic fields, electric currents parallel to 
the magnetic fields are known to be induced through the chiral anomaly, which is now 
called as the chiral magnetic effect. This effect gives the positive feed back so that the 
magnetic fields feels instability. In this talk, I discuss the realization of this mechanism
in the early Universe in which (hyper)magnetic fields are amplified. 
Especially I focus on how this effect is embedded in the cosmological magnetohydrodynamics 
and argue the fate of (hyper)magnetic fields and chiral asymmetry in the early Universe. 
The relations to the present intergalactic magnetic fields as well as the baryon
asymmetry of the Universe are also discussed. As an application, I show that the old SU(5)
GUT baryogenesis can be revived as the indirect origin of the present matter antimatter 
asymmetry through the (hyper)magnetic fields, otherwise the electroweak sphaleron process
will washout the asymmetry and spoil the mechanism.