Add new section describing the expected induced fluctuations in the primordial field as well as the coherent length scale of the induced (and external) primordial fields. Below is a copy of the referee report.
Report of the Referee -- DH13444/Steinmetz
The paper "Matter-antimatter origin of cosmic magnetism" presents a speculative new idea for the origin of primordial magnetisation, which is rooted in the development of the electron-positron plasma in the early Universe. While there is no proof of the main conjecture, equation (50) in the manuscript โ and no strong supporting heuristic argument โ this is a very interesting proposal that I believe deserves to be investigated further. The main concern I have is related to the topology of the magnetic field generated in this spontaneous magnetisation mechanism. Primordial magnetic fields generated in the early Universe are coherent only within the Hubble horizon at the time of generation, and this is much smaller than the current horizon today: in the proposed mechanism it is not clear what the spectrum of the magnetic field modes will be generated, and whether there is any helicity (another important factor that determines the subsequent equilibrium evolution of the magnetised plasma), see, e.g., https://inspirehep.net/literature/1225759. In order for this model to be considered a credible mechanism for primordial magnetogenesis I believe this point should be addressed.