Effects of biases in domain wall network evolution. II. Quantitative
  analysis
  Domain walls form at phase transitions which break discrete symmetries. In a
cosmological context they often overclose the universe (contrary to
observational evidence), although one may prevent this by introducing biases or
forcing anisotropic evolution of the walls. In a previous work [Correia {\it et
al.}, Phys.Rev.D90, 023521 (2014)] we numerically studied the evolution of
various types of biased domain wall networks in the early universe, confirming
that anisotropic networks ultimately reach scaling while those with a biased
potential or biased initial conditions decay. We also found that the analytic
decay law obtained by Hindmarsh was in good agreement with simulations of
biased potentials, but not of biased initial conditions, and suggested that the
difference was related to the Gaussian approximation underlying the analytic
law. Here we extend our previous work in several ways. For the cases of biased
potential and biased initial conditions we study in detail the field
distributions in the simulations, confirming that the validity (or not) of the
Gaussian approximation is the key difference between the two cases. For
anisotropic walls we carry out a more extensive set of numerical simulations
and compare them to the canonical velocity-dependent one-scale model for domain
walls, finding that the model accurately predicts the linear scaling regime
after isotropization. Overall, our analysis provides a quantitative description
of the cosmological evolution of these networks.
