Evolution of a domain wall in expanding universe: Inflation and after it

We study the evolution of thick domain walls in the expanding universe. We have found that the domain wall evolution crucially depends on the time-dependent parameter C(t) = 1/(H(t)0)2, where H(t) is the Hubble parameter and 0 is the width of the wall in flat space-time. For C(t) > 2 the physical width of the wall, a(t)(t), tends with time to constant value 0, which is microscopically small. Otherwise, when C(t) 2, the wall steadily expands and can grow up to a cosmologically large size.