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We study the evolution of the matter-antimatter asymmetry (Î·), the vorticity, and the hypermagnetic field in the symmetric phase of the early Universe, and in the temperature range 100ââGeVâ¤Tâ¤10ââTeV. We assume a configuration for the hypermagnetic field which includes both helical and nonhelical (Bz) components. Consequently, the hypermagnetic field and the fluid vorticity can directly affect each other, the manifestations of which we explore in three scenarios. In the first scenario, we show that in the presence of a small vorticity and a large Î·eR, helicity can be generated and amplified for an initially strong Bz. The generation of the helical seed is due to the chiral vortical effect and/or the advection term, while its growth is mainly due to the chiral magnetic effect which leads to the production of the baryon asymmetry, as well. The vorticity saturates to a nonzero value which depends on Bz, even in the presence of the viscosity, due to the backreaction of Bz on the plasma. Increasing the initial vorticity, makes the values of the helicity, Î·âs, and vorticity reach their saturation curves sooner, but does not change their final values at the onset of the electroweak phase transition. The second scenario is similar to the first except we assume that all initial Î·âs are zero. We find that much higher initial vorticity is required for the generation process and, while the values of Î·âs do not reach their saturation curves, final Î·âs of order 10â9 are possible. In the third scenario, we show that in the presence of only a strong hypermagnetic field, Î·âs and vorticity can be generated and amplified. Increasing the initial helicity increases the finalÎ·âs and vorticity. Although the values of Î·âs do not reach their saturation curves, final values of order 10â7 are possible. We find that although the presence of a nonzero initial Bz is necessary in all three scenarios, its increase only increases the final values of vorticity.
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