Scaling Density of Axion Strings

Abstract

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 zeta/t(2). The expectation has been that the dimensionless parameter zeta tends to a constant zeta(0), a feature of a string network known as scaling. It has recently been claimed that in larger numerical simulations zeta 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-zeta) 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 xi = t/root zeta, we find zeta(0) = 1.19 +/- 0.20. We conclude that the apparent corrections to zeta are artifacts of the initial conditions, rather than a property of the scaling network. The residuals from the constant-zeta (linear xi) 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%.