On the origin of cosmological magnetic fields

It is shown that a plasma with temperature T sustains fluctuations of electromagnetic fields and particle density even if it is assumed to be in a thermal equilibrium. The level of fluctuations in the plasma for a given wavelength and frequency of electromagnetic fields is rigorously computed by the fluctuation-dissipation theorem. A large zero frequency peak of electromagnetic fluctuations is discovered. We show that the energy contained in this peak is complementary to the energy ''lost'' by the plasma cutoff effect. The level of the zero frequency magnetic fields is computed as left-angle B2 right-angle 0/8π = 1/2π3 T(ωp/c)3, where T and ωp are the temperature and plasma frequency. This is the theoretical minimum magnetic field strength, as no turbulence is assumed. The size of the fluctuations is λ ∼ (c/ωp)(η/ω)1/2, where η and ω are the collision frequency and the frequency of magnetic fields oscillations. These results are not in contradiction with the conventional black-body radiation spectra but its extension, and as such, do not contradict the observed lack of structure in the cosmic microwave background. The level of these is computed Blambda = 9.4 x 10-7 (a/a0)-1/2 (λ/1 cm)-3/2 Gauss, where a and a0 are the scale factors at time t and at present and λ the wavelength of magnetic fluctuations. Our computer particle simulation shows the support of the theory and in fact exhibits a peaking of the magnetic energy spectrum at zero frequency. The level of magnetic fields is significant at the early radiation epoch of the Universe. Implications of these magnetic fields in the early Universe are discussed