Scaling in necklaces of monopoles and semipoles

Models of symmetry breaking in the early universe can produce networks of cosmic strings threading ’t Hooft-Polyakov monopoles. In certain cases there is a larger global symmetry group and the monopoles split into so-called semipoles. These networks are all known as cosmic necklaces. We carry out large-scale field theory simulations of the simplest model containing these objects, confirming that the energy density of networks of cosmic necklaces approaches scaling, i.e., that it remains a constant fraction of the background energy density. The number of monopoles per unit comoving string length is constant, meaning that the density fraction of monopoles decreases with time. Where the necklaces carry semipoles rather than monopoles,we perform the first simulations large enough to demonstrate that they also maintain a constant number per unit comoving string length. We also compare our results to a number of analytical models of cosmic necklaces, finding that none explains our results. We put forward evidence that annihilation of poles on the strings is controlled by a diffusive process, a possibility not considered before. The observational constraints derived in our previous work for necklaces with monopoles can now be safely applied to those with semipoles as well.