2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/42158Thermal 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.5 pages, updated to match the version published in PRD (http://link.aps.org/abstract/PRD/v68/e021301) on 11 July 2003High Energy Physics - PhenomenologyAstrophysicstext