This paper examines the problem of the string decay contribution to the axion cosmological energy density. We show that this contribution is proportional to the average relative increase when axion strings decay of a certain quantity $N_{\mathrm{ax}}$ which we define. We carry out numerical simulations of the evolution and decay of circular and non-circular string loops, of bent strings with ends held fixed, and of vortex-antivortex pairs in two dimensions. In the case of string loops and of vortex-antivortex pairs, $N_{\mathrm{ax}}$ decreases by approximately 20%. In the case of bent strings, $N_{\mathrm{ax}}$ remains constant or increases slightly. Our results imply that the string decay contribution to the axion energy density is of the same order of magnitude as the well-understood contribution from vacuum realignment.

• Received 11 January 2001

DOI:https://doi.org/10.1103/PhysRevD.63.125018