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Monopole annihilation in cosmic necklaces

A sequence of two symmetry breaking transitions in the early universe may produce monopoles whose flux is confined into two strings each, which thus assemble into "necklaces" with monopoles as beads. Such "cosmic necklaces" have been proposed as a source of ultra-high-energy cosmic rays. We analyze the evolution of these systems and show that essentially all monopoles annihilate or leave the string at early times, after which cosmic necklaces evolve in a similar way to a network of ordinary cosmic strings. We investigate several modifications to the basic picture, but in nearly all cases we find that too few monopoles remain on the necklaces to produce any observable cosmic rays. There may be a small window for superconducting condensates to prevent annihilations, but only if both the string and the condensate scale are very high.