understand this is to realize that when $\epsilon_1 \neq 0$ one is actually considering a situation similar to a first order phase transition. As domain walls keep intersecting each other and pinching off, one can consider closed domain walls at any given time. The whole region then looks like bubbles of one phase embedded in the other other. The bubbles which have $\theta = \pi$ inside will always shrink, while the bubbles which have $\theta = 0$ inside should expand, but only if the size of such bubbles is larger than a critical size $R_c$. This critical size can be determined by considering the total energy $E_R$ of a bubble of radius $R$, $$E_R = - {4\pi \over 3} R^3 \Delta \rho_V + 4\pi R^2 \rho_S \, .$$ The critical size $R_c$ is determined by requiring that $E_R$ be stationary with respect to small variations in $R$. Bubbles larger than $R_c$, which have $\theta = 0$ inside, will expand while those smaller than $R_c$ will collapse. We find that $$R_c = {2\rho_S \over \Delta \rho_V} \,=\,
v {{\sqrt \epsilon_2} \over \epsilon_1} \, .$$

So far we have neglected the fact that the Universe is expanding. If $R_c$, at a given 