Accurate Calibration of the Velocity-dependent One-scale Model for Domain Walls

Abstract

We study the asymptotic scaling properties of standard domain wall networks in several cosmological epochs. We carry out the largest field theory simulations achieved to date, with simulation boxes of size 20483, and confirm that a scale-invariant evolution of the network is indeed the attractor solution. The simulations are also used to obtain an accurate calibration for the velocity-dependent one-scale model for domain walls: we numerically determine the two free model parameters to have the values $c_w = 0.34\pm0.16$ and $k_w = 0.98\pm0.07$, which are higher precision than (but in agreement with) earlier estimates.