Approach to scaling in axion string networks

Understand

We study the approach to scaling in axion string networks in the radiation era, 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.
• The string length has also been commonly expressed in terms of a dimensionless string length density $\zeta$, proportional to the number of Hubble lengths of string per Hubble volume.