Scaling properties of cosmological axion strings

There has been recent interest in the evolution and cosmological consequences of global axionic string networks, and in particular in the issue of whether or not these networks reach the scale-invariant scaling solution that is known to exist for the simpler Goto-Nambu and Abelian-Higgs string networks. This is relevant for determining the amount and spectrum of axions they produce. We use the canonical velocity-dependent one-scale model for cosmic defect network evolution to study the evolution of these global networks, confirming the presence of deviations to scale-invariant evolution and in agreement with the most recent numerical simulations. We also quantify the cosmological impact of these corrections and discuss how the model can be used to extrapolate the results of numerical simulations, which have a limited dynamic range, to the full cosmological evolution of the networks, enabling robust predictions of their consequences. Our analysis suggests that around the QCD scale, when the global string network is expected to disappear and produce most of the axions, the number of global strings per Hubble patch should be around $\xi\sim4.2$, but also highlights the need for additional high-resolution numerical simulations.