Parameter-free velocity-dependent one-scale model for domain walls
Pedro Pina Avelino · Physical review. D/Physical review. D. · 2020
We develop a parameter-free velocity-dependent one-scale model for the evolution of the characteristic length $L$ and root-mean-square velocity ${\ensuremath{\sigma}}_{v}$ 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 $t$ ($a\ensuremath{\propto}{t}^{\ensuremath{\lambda}}$, $0<\ensuremath{\lambda}<1$), with the corresponding results obtained using field theory numerical simulations. We show that they agree well (within a few %) for root-mean-square velocities ${\ensuremath{\sigma}}_{v}$ smaller than $0.2c$ ($\ensuremath{\lambda}\ensuremath{\ge}0.9$), where $c$ is the speed of light in vacuum, but significant discrepancies occur for larger values of ${\ensuremath{\sigma}}_{v}$ (smaller values of $\ensuremath{\lambda}$). We identify problems with the determination of $L$ and ${\ensuremath{\sigma}}_{v}$ from numerical field theory simulations which might potentially be responsible for these discrepancies.