Evolution of thick domain walls in inflationary and p = wρ 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 = wρ. We have found that the domain wall evolution crucially depends on the time-dependent parameter C(t) = 1/(H(t)δ₀)², where H(t) is the Hubble parameter and δ₀ is the thickness of the wall in flat space-time. For C(t) > 2 the physical thickness of the wall, a(t)δ(t), tends with time to δ₀, which is microscopically small. Otherwise, when C(t) ≤ 2, the wall steadily expands and can grow up to a cosmologically large size. (orig.)