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Gravitational waves from the evolution of magnetic field after electroweak epoch

It was recently demonstrated that the evolution of helical magnetic field in the primordial plasma at temperatures $T\gtrsim10$ MeV is affected by the phenomenon of chiral quantum anomaly in the electroweak model, leading to a possibility of self-sustained existence of magnetic field and chiral asymmetry in the electronic distribution. This may serve as a mechanism for generating primordial magnetic field in the early universe. Violent magnetic-field generation may lead to production of gravitational waves which, regardless of the fate of magnetic field itself, survive until today. We estimate the threshold value of the initial chiral asymmetry above which the generated gravitational waves would affect the big-bang nucleosynthesis and would show up in the current and future experiments on gravitational-wave detection.