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 σ_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 ∝t^λ, 0 <λ <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 σ_v smaller than 0.2 c (λ ≥0.9 ), where c is the speed of light in vacuum, but significant discrepancies occur for larger values of σ_v (smaller values of λ ). We identify problems with the determination of L and σ_v from numerical field theory simulations which might potentially be responsible for these discrepancies.