We investigate the cosmological consequences of particle physics theories that admit stable loops of superconducting cosmic string - {\it vortons}. General symmetry breaking schemes are considered, in which strings are formed at one energy scale and subsequently become superconducting in a secondary phase transition at what may be a considerably lower energy scale. We estimate the abundances of the ensuing vortons, and thereby derive constraints on the relevant particle physics models from cosmological observations. These constraints significantly restrict the category of admissible Grand Unified theories, but are quite compatible with recently proposed effects whereby superconducting strings may have been formed close to the electroweak phase transition.

33 pages, 2 figures, RevTeX