Domain Walls in the Early Universe and Generation of Matter and Antimatter Domains

We present a model where it is possible to generate cosmologically large domains of matter and antimatter separated by cosmologically large distances. Domain walls existed only in the early universe and later they disappeared. So the problem of domain walls in this model does not exist. These features are achieved through a postulated form of interaction between inflaton and a new scalar field. This scenario inspired a study of the related problem - evolution of the domain wall width in expanding universe. According to classical results there is a region of parameter space where the solutions with constant physical width exist. Numerical study of the problem demonstrates that initial configurations tend to these solutions with time. However, we have found that the wall width can grow exponentially outside of that parameter region