Magnetobaryogenesis in the presence of weak sphalerons from overlapping transient fluctuations in temperature and vorticity

We show how the temperature-dependent chiral vortical effect can generate hypermagnetic fields and matter-antimatter asymmetries, in the symmetric phase of the early Universe, in the temperature range 100GeV<T<10TeV, even in the presence of the weak sphaleron processes. We take into account all perturbative chirality-flip processes, as well as the nonperturbative Abelian and non-Abelian anomalous effects. By considering the resulting constraints and conservation laws in the plasma, we reduce the number of required evolution equations. We also simplify the anomalous transport coefficients, accordingly. We then show that, due to the overlapping small transient fluctuations in the temperature of some matter degrees of freedom and vorticity of the plasma, the emergent chiral vortical current leads to the generation of strong hypermagnetic fields and matter-antimatter asymmetries, all starting from zero initial values. We obtain the baryon asymmetry 10^(-10) and a positive helicity hypermagnetic field with the amplitude 10^(19)G, at the onset of the electroweak phase transition. Although the sphaleron processes tend to washout the generated (B+L) asymmetry, the hypermagnetic field impedes the washout process, and the baryogenesis and leptogenesis occur without (B-L) violation.