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Relic gravitational waves (GWs) can be produced by primordial magneticfields. However, not much is known about the resulting GW amplitudes and theirdependence on the details of the generation mechanism. Here we treat magneticfield generation through the chiral magnetic effect (CME) as a genericmechanism and explore its dependence on the speed of generation (the product ofmagnetic diffusivity and characteristic wavenumber) and the speedcharacterizing the maximum magnetic field strength expected from the CME. Whenthe latter exceeds the former (regime I), the regime applicable to the earlyuniverse, we obtain an inverse cascade with moderate GW energy that scales withthe third power of the magnetic energy. When the generation speed exceeds theCME limit (regime II), the GW energy continues to increase without acorresponding increase of magnetic energy. In the early kinematic phase, the GWenergy spectrum (per linear wavenumber interval) has opposite slopes in bothregimes and is characterized by an inertial range spectrum in regime I and awhite noise spectrum in regime II. The occurrence of these two slopes is shownto be a generic consequence of a nearly monochromatic exponential growth of themagnetic field. The resulting GW energy is found to be proportional to thefifth power of the limiting CME speed and the first power of the generationspeed.

Relic gravitational waves from the chiral magnetic effect