Thermal production of superheavy magnetic monopoles in the early universe

Starting with an initial abundance of zero, we calculate the thermal production of magnetic monopoles by using the monopole-antimonopole annihilation cross section and detailed balance. The final abundance of monopoles depends exponentially upon m/T_i; m is the monopole mass ～10¹⁶ GeV and T_i is the temperature when production commences. For m/T_i ≈35–55 the present monopole to photon ratio is nM/n_γ≈10^?23?10^?38, less than the bound derived from the present mass density, but possibly large enough to be detected. This calculation provides a lower bound on the monopole abundance for a given m/T_i.