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Why do we observe magnetic fields in the sky? Why do we live in a magnetized Universe? A variety of observations imply that stars, planets, galaxies, clusters of galaxies are all magnetized. The typical magnetic field strengths (2) range from few µ G (in the case of galaxies and galaxy clusters) to few G (in the case of planets, like the earth) up to 1012 G (in the case of neutron stars). Physical phenomena are characterized depending upon the typical time and length scales where they take place. Magnetic fields of stars and planets are related to length-scales which are much smaller than the diameter of the Milky Way (of the order of 30 Kpc) or of the local supercluster. In this sense, a magnetic field of the order of µ G is minute on the terrestrial scale but it is sizable over the scale of the supercluster.

In the present review only large-scale magnetic fields will be considered, i.e. magnetic fields whose typical scale exceeds the AU (1 AU = 1.49 × 1013 cm). Large-scale magnetic fields must be understood and treated as an essential part of the largest structures observed in the sky. Legitimate questions arising in the study of magnetized structures concern their formation and evolution. The answers to these questions are still not completely settled. Specific observations will eventually allow to discriminate between the different competing explanations.

Magnetic fields of distant spiral galaxies are in the µ G range. There is also compelling evidence of large-scale magnetic fields which are not associated with individual galaxies. This empirical coincidence reminds a bit of one of the motivations of the standard hot big-bang model, namely the observation that the light elements are equally abundant in rather different parts of our Universe. The approximate equality of the abundances implies that, unlike the heavier elements, the light elements have primordial origin. The four light isotopes D, 3He, 4He and 7Li are mainly produced at a specific stage of the hot big bang model named nucleosynthesis occurring below the a typical temperature of 0.8 MeV when neutrinos decouple from the plasma and the neutron abundance evolves via free neutron decay. The abundances calculated in the simplest big-bang nucleosythesis model agree fairly well with the astronomical observations. In similar terms it is plausible to argue that large-scale magnetic fields have similar strengths at large scales because the initial conditions for their evolutions were the same, for instance at the time of the gravitational collapse of the protogalaxy. The way the initial conditions for the evolution of large-scale magnetic fields are set is generically named magnetogenesis.

There is another comparison which might be useful. Back in the seventies the so-called Harrison-Zeldovich spectrum was postulated. Later, with the developments of inflationary cosmology the origin of a flat spectrum of curvature and density profiles has been justified on the basis of a period of quasi-de Sitter expansion named inflation. It is plausible that in some inflationary models not only the fluctuations of the geometry are amplified but also the fluctuations of the gauge fields. This happens if, for instance, gauge couplings are effectively dynamical. As the Harrison-Zeldovich spectrum can be used as initial condition for the subsequent Newtonian evolution, the primordial spectrum of the gauge fields can be used as initial condition for the subsequent magnetohydrodynamical (MHD) evolution which may lead, eventually, to the observed large-scale magnetic fields.

Cosmologists and theoretical physicists would like to understand large-scale magnetization in terms of symmetries which are broken. There are other two different motivations leading, independently, to the study of large-scale magnetic fields. For instance it was observed long ago by Fermi that if cosmic rays are in equilibrium with the galaxy, their pressure density is comparable with the one of the magnetic field of the galaxy. Large-scale magnetic fields are also extremely relevant for astrophysics. Magnetic fields in galaxies are sufficiently intense to affect the dynamics of interstellar gas both on the galactic scale and also on smaller scales characteristic of star formation processes. This is the third motivation leading to the study of large scale-magnetic fields: the astrophysical motivation which tries to combine our knowledge of the Universe in powerful dynamical principles based on the microscopic laws of nature.

The cross-disciplinary character of the physical phenomena addressed in this review is apparent from the table of content. In Section 2 a brief historical account of this fifty years old problem will be given. Then, to clarify the nature of the various theoretical constructions, the empirical evidence of large scale magnetic fields will be discussed in Section 3. Section 4 contains some background material on the evolution of magnetic fields in globally neutral plasmas in flat space. Section 5 and 6 address the problem of the evolution of large scale magnetic fields in curved backgrounds and of their origin. In Section 7 the possible effects of magnetic fields on the thermodynamical history of the Universe are scrutinized. Section 8 will be concerned with the effects of large scale magnetic fields on the Cosmic Microwave Background radiation (CMB) and on the relic background of gravitational waves. In Section 9 the rôle of gravitating magnetic fields in cosmological solutions will be swiftly pointed out.

The perspective of present review is theoretical. In this sense various (very important) experimental results (for instance concerning optical polarization) will receive only a swift attention.

2 In this review magnetic fields will be expressed in gauss. In the SI units 1 T = 104 G. For practical reasons, in cosmic ray physics and in cosmology it is also useful to express the magnetic field in GeV2 (in units hbar = c = 1). Recalling that the Bohr magneton is about 5.7 × 10-11 MeV / T the conversion factor will then be 1 G = 1.95 × 10-20 GeV2. Back.

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