Magnetic field spectrum in a plasma in thermal equilibrium in the epoch of primordial nucleosynthesis

The low-frequency magnetic field spectrum in the primordial plasma is of particular interest as a possible origin of magnetic fields in the universe (e.g., Tajima and co-workers and Cable and Tajima). We derive the magnetic field spectrum in the primordial plasma, in particular, at the epoch of primordial nucleosynthesis. The pioneering study of Cable and Tajima of the electromagnetic fluctuations, based on the fluctuation-dissipation theorem, is extended. Our model describes both the thermal and collisional effects in a plasma. It is based on a kinetic description with the Bhatnagar, Gross, and Krook (BGK) collision term. It is shown that the zero-frequency peak found by Cable and Tajima decreases. At high frequencies, the blackbody spectrum is obtained naturally without the necessity of the link procedure used by them. At low frequencies $(\omega <~4{\omega }_{\mathrm{pe}},$ where ${\omega }_{\mathrm{pe}}$ is the electron plasma frequency), it is shown that the magnetic field spectrum has more energy than the blackbody spectrum in vacuum.