To study the validity of the horizon bound on the annihilation rate of primordial magnetic monopoles, we investigate the initial configurations of a two-dimensional model of vortices connected by strings suggested by Everett, Vachaspati, and Vilenkin. The length distributions of open strings are obtained from Monte Carlo simulations and are shown to agree with distributions derived from probability arguments. The length distributions of closed strings are found and are shown to agree with a derived formula containing no adjustable parameters. The evolution of the configurations is discussed.

• Received 28 June 1990

DOI:https://doi.org/10.1103/PhysRevD.42.3422