Evolution of thick domain walls in inflationary and $p=w\rho$ universe

We study the evolution of thick domain walls in the different models of cosmological inflation, in the matter-dominated and radiation-dominated universe, or more generally in the universe with the equation of state $p=w\rho$. We have found that the domain wall evolution crucially depends on the time-dependent parameter $C(t)=1/(H(t)\delta_0)^2$, where $H(t)$ is the Hubble parameter and $\delta_0$ is the thickness of the wall in flat space-time. For $C(t)>2$ the physical thickness of the wall, $a(t)\delta(t)$, tends with time to $\delta_0$, which is microscopically small. Otherwise, when $C(t) \leq 2$, the wall steadily expands and can grow up to a cosmologically large size.