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

TL;DR

This paper uses large-scale simulations to confirm the scale-invariant evolution of domain wall networks and provides a precise calibration of the velocity-dependent one-scale model parameters.

Contribution

It offers the largest field theory simulations to date and accurately calibrates the velocity-dependent one-scale model for domain walls.

Findings

Confirmed scale-invariant evolution as the attractor solution.

Provided precise numerical values for model parameters.

Validated previous estimates with higher accuracy.

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.