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.
