Relic axions radiated from axionic strings

We investigate the evolution of the global(axionic) string network in the radiation dominated universe by use of numerical simulations in 3+1 dimensions. We find that the global string network settles down to the scaling regime where the energy density of global strings, rho (s), is given by rho (s) = xi mu /t(2) with mu the string tension per unit length and the scaling parameter, xi similar to (1.00 +/- 0.08), irrespective of the cosmic time. We also find that the loop distribution function can be fitted with that predicted by the so-called one scale model. Concretely, the number density, n(l)(t), of the loop with the length, l, is given by nt(t) = nu/[t(3/2)(l + nt)(5/2)] where nu similar to 0.0865 and kappa is related with the Nambu-Goldstone(NG) boson(axion) radiation power from global(axionic) strings, P, as P = KM with rc similar to 0.535. Therefore, the loop production function also scales and the typical scale of produced loops is nearly the horizon distance. Thus, the evolution of the global(axionic) string network in the radiation dominated universe can be well described by the one scale model in contrast with that of the local string network. Furthermore, the power spectrum of axions radiated from axionic strings is calculated from the simulation data, which is found to be highly peaked around the Hubble scale, and a more accurate constraint on the Peccei-Quinn breaking scale is obtained.