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6.4. Mixed mechanisms

From the above discussion it is apparent that the mechanisms producing magnetic fields at some moment in the life of the Universe (and inside the Hubble radius) have to justify the large correlation scale of the magnetic seeds required by subsequent MHD considerations. The possibility of turbulent behaviour in the early Universe, even though physically justified, seems to be difficult to quantify even if rather reasonable quantitative estimates appeared so far. On the other hand, inflationary scenarios can lead to magnetic seeds with large correlation scale.

A useful point to be stressed is that there may exist "mixed" mechanisms. Consider the following example which has been proposed in [171] and [172]. Suppose that during the inflationary phase a stochastic background of gauge fields is produced thanks to the breaking of conformal invariance. The spectral amplitude of the generated field will be constrained by the critical density bound and by all the other dynamical considerations related to the finite values of the diffusion scales.

The generated magnetic field spectrum will be distributed over a large interval of frequencies. In particular, the energy spectrum of the magnetic field will be non negligible at some intermediate scale, like, for instance, the electroweak scale, i.e. the physical frequency omegaew ~ Hew. In other words, if magnetic fields are generated thanks to some inflationary mechanism, the amplified magnetic inhomogeneities will be reentering at different epochs during the radiation dominated phase and the scales which left the horizon later during inflation will reenter earlier.

Given the background of abelian gauge fields, the dynamics of the electroweak epoch may add interesting physical features. For instance the magnetic field of inflationary origin will be, as discussed, topologicaly trivial: its magnetic gyrotropy will vanish. However, during the EW epoch, thanks to a pseudoscalar vertex due either to a pseudo goldstone boson or to the chemical pootential, the topologically trivial hypermagnetic background may be turned into a topologically non-trivial background and large magnetic helicity may be generated.

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