Scaling Density of Axion Strings

In the QCD axion dark matter scenario with postinflationary Peccei-Quinn symmetry breaking, the number density of axions, and hence the dark matter density, depends on the length of string per unit volume at cosmic time t, by convention written ζ/t^{2}. The expectation has been that the dimensionless parameter ζ tends to a constant ζ_{0}, a feature of a string network known as scaling. It has recently been claimed that in larger numerical simulations ζ shows a logarithmic increase with time, while theoretical modeling suggests an inverse logarithmic correction. Either case would result in a large enhancement of the string density at the QCD transition, and a substantial revision to the axion mass required for the axion to constitute all of the dark matter. With a set of new simulations of global strings, we compare the standard scaling (constant-ζ) model to the logarithmic growth and inverse-logarithmic correction models. In the standard scaling model, by fitting to linear growth in the mean string separation ξ=t/sqrt[ζ], we find ζ_{0}=1.19±0.20. We conclude that the apparent corrections to ζ are artifacts of the initial conditions, rather than a property of the scaling network. The residuals from the constant-ζ (linear ξ) fit also show no evidence for logarithmic growth, restoring confidence that numerical simulations can be simply extrapolated from the Peccei-Quinn symmetry-breaking scale to the QCD scale. Reanalysis of previous work on the axion number density suggests that recent estimates of the axion dark matter mass in the postinflationary symmetry-breaking scenario we study should be increased by about 50%.