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 (or nearly zero) frequency magnetic fields is computed as <B2>0/8-pi = [T(omega(p)/c)3]/(2-pi-3), where T and omega-p are the temperature and plasma frequency. This is the theoretical minimum magnetic field strength spontaneously generated, as no turbulence is assumed. The size of the fluctuations is lambda approximately (c/omega(p))(eta/omega)1/2, where eta and omega are the collision frequency and the (nearly zero) frequency of magnetic fields oscillations. The results are not in contradiction with the conventional blackbody radiation spectra but its extension, and as such, do not contradict the observed lack of structure in the cosmic microwave background. 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. Such magnetic fluctuations provide seed fields for later evolution. Implications of these magnetic fields in the early universe (t = 10(-2)-10(13) s) are discussed.