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 )δ0 )2 , where H (t ) is the Hubble parameter and δ0 is the width of the wall in flat space-time. For C (t ) > 2 the physical width of the wall, a (t )δ (t ), tends with time to constant value δ 0 , which is microscopically small. Otherwise, when C (t ) ≤ 2, the wall steadily expands and can grow up to a cosmologically large size.