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 \sim 4.2 , but also highlights the need for additional high-resolution numerical simulations .