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We study the evolution of the matter-antimatter asymmetry ({\eta}), thevorticity, and the hypermagnetic field in the symmetric phase of the earlyUniverse, and in the temperature range 100 GeV < T < 10 TeV. We assume aconfiguration for the hypermagnetic field which includes both helical andnon-helical (Bz) components. Consequently, the hypermagnetic field and thefluid vorticity can directly affect each other, the manifestations of which weexplore in three scenarios. In the first scenario, we show that in the presenceof a small vorticity and a large {\eta}eR, helicity can be generated andamplified for an initially strong Bz. The generation of the helical seed is dueto the chiral vortical effect (CVE) and/or the advection term, while its growthis mainly due to the chiral magnetic effect (CME) which leads to the productionof the baryon asymmetry, as well. The vorticity saturates to a nonzero valuewhich depends on Bz, even in the presence of the viscosity, due to theback-reaction of Bz on the plasma. Increasing the initial vorticity, makes thevalues of the helicity, {\eta}s, and vorticity reach their saturation curvessooner, but does not change their final values at the onset of the electroweakphase transition. The second scenario is similar to the first except we assumethat all initial {\eta}s are zero. We find that much higher initial vorticityis required for the generation process. In the third scenario, we show that inthe presence of only a strong hypermagnetic field, {\eta}s and vorticity can begenerated and amplified. Increasing the initial helicity, increases the final{\eta}s and vorticity. We find that although the presence of a nonzero initialBz is necessary in all three scenarios, its increase only increases the finalvalues of vorticity.

The effects of non-helical component of hypermagnetic field on the evolution of the matter-antimatter asymmetry, vorticity, and hypermagnetic field