Extending the velocity-dependent one-scale model for domain walls
  We report on an extensive study of the evolution of domain wall networks in Friedmann-Lema\^{\i}tre-Robertson-Walker universes by means of the largest currently available field-theory simulations. These simulations were done in $4096^3$ boxes and for a range of different fixed expansion rates, as well as for the transition between the radiation and matter eras. A detailed comparison with the velocity-dependent one-scale (VOS) model shows that this cannot accurately reproduce the results of the entire range of simulated regimes if one assumes that the phenomenological energy loss and momentum parameters are constants. We therefore discuss how a more accurate modeling of these parameters can be done, specifically by introducing an additional mechanism of energy loss (scalar radiation, which is particularly relevant for regimes with relatively little damping) and a modified momentum parameter which is a function of velocity (in analogy to what was previously done for cosmic strings). We finally show that this extended model, appropriately calibrated, provides an accurate fit to our simulations. 
C. J. A. P. Martins, I. Yu. Rybak, A. Avgoustidis, E. P. S. Shellard
hep-ph astro-ph.CO gr-qc hep-th