On the Origin of Cosmological Magnetic Fields

Abstract

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 ${\left\langle {{B^2}} \right\rangle ^0}/8\pi = \frac{1}{{2{\pi ^3}}}T{({\omega _p}/c)^3}$, where T and ω _P 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 $\lambda {\rm{ }} \sim (c/{\omega _p}){(\eta \tau )^{1/2}}$, where η and T are the collision frequency and the lifetime of magnetic fields fluctuations. The level of magnetic fields is significant at the early radiation epoch of the Universe: Magnetic fields as great as 10¹⁶ Gauss is generated at t = 10^-2 sec.