### Speaker

### Description

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 $\zeta/t^2$. 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. This 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. We also study the approach to scaling, through measuring the root-mean-square velocity $v$ as well as the scaled mean string separation $x$. We find good evidence for a fixed point in the phase-space analysis in the variables $(x,v)$, providing a strong indication that standard scaling is taking place. We show that the approach to scaling can be well described by a two parameter velocity-one-scale (VOS) model, and show that the values of the parameters are insensitive to the initial state of the network. We conclude that the apparent corrections to $\zeta$ are artifacts of the initial conditions, rather than a property of the scaling network.