  Thermal fluctuations of the gauge field lead to monopole formation at the
grand unified phase transition in the early Universe, even if the transition is
merely a smooth crossover. The dependence of the produced monopole density on
various parameters is qualitatively different from theories with global
symmetries, and the monopoles have a positive correlation at short distances.
The number density of monopoles may be suppressed if the grand unified symmetry
is only restored for a short time by, for instance, nonthermal symmetry
restoration after preheating.
