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We discuss some old and new results on mangetic fields GeneralitiesMagnetic fields are everywhere.Magnetic fields are stable, and hence they could exists since inflation times, or even earlier. Stability is only approximate, a magnetic field will decay if stronger than B = 10 2 4 Gauss. This is so because the Lorentz force cannot perform any work on charged spin half particles so that real particle-antiparticles free pairs cannot be produced. Elementary W bosons are coupled in a momemtum independent way to the field and can provoke its decay. This is the energy corresponding to creation of a W pair 10 24 Gauss. We look into this now in some detail. Notice that the electric field is unstable at a comparably very low energy determined by electron positron tunneling. This is the celebrated Schwinger tunneling. Magnetic fields and the electroweak vacuumIt was pointed out by Ambjorn and Olesen [14] (see also Ref. [15]) that the Weinberg-Salam model of electroweak interactions shows an instability at B 10 24 Gauss. The nature of such instability can be understood by looking at the expression of the energy of a particle with electric charge e, and spin s, moving in homogeneous magnetic field B directed along the z-axis. Above a critical field B c = m 2 /e particle energy is discretized into Landau levelsWe observe that energy of scalar (s = 0) and spinor (s z = ±1/2) is always positive, and indeed no instability arise in QED (it is possible to verify that quantum one-loop corrections do not spoil this conclusion). In the case of vector particles (s z = 0, ±1), * Speaker.

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We consider the possibility of generation of the seeds of primordial magnetic field on inflation and show that the effect of the back reaction of this field can be very important. Assuming that back reaction does not spoil inflation we find a rather strong restriction on the amplitude of the primordial seeds which could be generated on inflation. Namely, this amplitude recalculated to the present epoch cannot exceed 10 −32 G in M pc scales. This field seems to be too small to be amplified to the observable values by galactic dynamo mechanism.

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We put bounds on the variation of the value of the fine structure constant α, at the time of Big Bang nucleosynthesis. We study carefully all light elements up to 7 Li. We correct a previous upper limit on |∆α/α| estimated from 4 He primordial abundance and we find interesting new potential limits (depending on the value of the baryon-to-photon ratio) from 7 Li, whose production is governed to a large extent by Coulomb barriers. The presently unclear observational situation concerning the primordial abundances preclude a better limit than |∆α/α| ∼ < 2 · 10 −2 , two orders of magnitude less restrictive than previous bounds. In fact, each of the (mutually exclusive) scenarios of standard Big Bang nucleosynthesis proposed, one based on a high value of the measured deuterium primordial abundance and one based on a low value, may describe some aspects of data better if a change in α of this magnitude is assumed.

In this paper we study the effect of a magnetic field on the fluctuation spectrum of the cosmic microwave background. We find that upcoming measurements might give interesting bounds on large scale magnetic fields in the early Universe. If the effects are seen, it might be possible to establish the presence of different fields in different patches of the sky. Absence of any effect, will provide by one order of magnitude a better limit for a primordial field, now given by nucleosynthesis.