Parameter-free velocity-dependent one-scale model for domain walls

We develop a parameter-free velocity-dependent one-scale model for the evolution of the characteristic length $L$ and root-mean-square velocity $\sigma_v$ of standard domain wall networks in homogeneous and isotropic cosmologies. We compare the frictionless scaling solutions predicted by our model, in the context of cosmological models having a power law evolution of the scale factor $a$ as a function of the cosmic time $t$ ($a \propto t^\lambda$, $0< \lambda < 1$), with the corresponding results obtained using field theory numerical simulations. We show that they agree well (within a few $\%$) for root-mean-square velocities $\sigma_v$ smaller than $0.2 \, c$ ($\lambda \ge 0.9$), where $c$ is the speed of light in vacuum, but significant discrepancies occur for larger values of $\sigma_v$ (smaller values of $\lambda$). We identify problems with the determination of $L$ and $\sigma_v$ from numerical field theory simulations which might potentially be responsible for these discrepancies.