In the QCD axion dark matter scenario with post-inflationary 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 ζ0, 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 modelling 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/ √ ζ, we find ζ0 = 1.19 ± 0.20. The linear fit to ξ in standard scaling model also allows a time offset, t0, which takes into account the initial string evolution. We show that the convergence of ζ to its scaling value depends on t0, that the coefficients of the logarithm and inverse-logarithm are consistent with zero when t0/t f → 0, where t f is the final time of the fit, and that the constant terms in the models are consistent with the standard scaling measurement. We conclude that the apparent growth in ζ is an artefact of the time offset in 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. Re-analysis of previous work on the axion number density suggests that recent estimates of the axion dark matter mass in the post-inflationary symmetry-breaking scenario we study should be increased by about 50%.
Introduction:The Peccei-Quinn (PQ) mechanism, which solves the strong CP problem of QCD by extending the Standard Model with an extra U(1) global symmetry [1], brings with it a long-lived pseudoscalar particle, the axion [2]. A universe where light axions [3,4] constitute the dark matter [5] is one of the most promising scenarios in the current cosmological paradigm.If the PQ symmetry is spontaneously broken after primordial inflation, axion strings are formed [6], a variety of global cosmic string [7,8]. They survive until the QCD confinement transition at around 150 MeV, when they become connected by domain walls made of the CP-odd gluon condensate [9,10], and are annihilated. Most of the energy is left behind in the form of axion radiation, produced through the lifetime of the string network and during the annihilation phase. The axion radiation can also be viewed as light massive particles, whose number density depends on the length of string per unit ...