Published in Physics Reports, Vol. 348, Issue 3, pp. 163-266.

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Dario Grasso 1 and Hector R. Rubinstein 2

1 Dipartimento di Fisica "G. Galilei", Università di Padova,
Via Marzolo, 8, I-35131 Padova, Italy,

I.N.F.N. Sezione di Padova.
2 Department of Theoretical Physics, Uppsala University,
Box 803, S-751 08 Uppsala, Sweden,
Fysikum, Stockholm University, Box 6730, 113 85 Stockholm, Sweden.

Abstract. This review concerns the origin and the possible effects of magnetic fields in the early Universe. We start by providing to the reader with a short overview of the current state of art of observations of cosmic magnetic fields. We then illustrate the arguments in favour of a primordial origin of magnetic fields in the galaxies and in the clusters of galaxies. We argue that the most promising way to test this hypothesis is to look for possible imprints of magnetic fields on the temperature and polarization anisotropies of the cosmic microwave background radiation (CMBR). With this purpose in mind, we provide a review of the most relevant effects of magnetic fields on the CMBR. A long chapter of this review is dedicated to particle physics inspired models which predict the generation of magnetic fields during the early Universe evolution. Although it is still unclear if any of these models can really explain the origin of galactic and intergalactic magnetic fields, we show that interesting effects may arise anyhow. Among these effects, we discuss the consequences of strong magnetic fields on the big-bang nucleosynthesis, on the masses and couplings of the matter constituents, on the electroweak phase transition, and on the baryon and lepton number violating sphaleron processes. Several intriguing common aspects, and possible interplay, of magnetogenesis and baryogenesis are also dicussed.

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