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The topics reported in the present review suggest various open problems on the nature of large-scale magnetic fields in the present and in the early Universe:

It would be important, for the theorist, a reasonable accuracy (within one order of magnitude) in the experimental determination of large-scale magnetic fields. For instance even one order of magnitude in the intensity of the intra-cluster magnetic field (i.e. 10-6 G rather than 10-7 G) makes a difference as far as the problem of the origin is concerned. In the same perspective, more accurate determinations of the typical correlation scales of the intra-cluster fields would be desirable.

There is, at the moment, no compelling reason why large-scale magnetic fields should not be primordial, at least to some degree:

In the next decade a progress of the empirical knowledge is expected in apparently unrelated areas like x and gamma-ray astronomy, radio-astronomy, CMB physics, detection of relic gravitational waves. All these areas are connected with the existence and with the properties of large-scale magnetic fields in the early and in the present Universe. This connection is sometimes rather fragile since it is mediated by various theoretical assumptions. However, there is the hope that, in a not too distant future, some of the puzzles related to the origin and existence of large-scale magnetic fields may be resolved and some of the current theoretical guessworks firmly ruled out.


Some of the ideas presented in this review have been elaborated and assembled on the occasion of different sets of lectures delivered through the years. The author wishes to express his gratitude to D. Babusci, H. de Vega, M. Gasperini, H. Kurki-Suonio, E. Keihänen, N. Sanchez, M. Shaposhnikov, G. Veneziano, A. Vilenkin. A special thank is due to G. Cocconi for important remarks which improved the first draft.

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