Domain Walls and Matter-Antimatter Domains in the Early Universe

We suggest a scenario of spontaneous (or dynamical) C and CP violation according to which it is possible to generate domains of matter and antimatter separated by cosmologically large distances. Such C(CP) violation existed only in the early universe and later it disappeared with the only trace of generated matter and antimatter domains. So this scenario does not suffer from the problem of domain walls. According to this scenario the width of the domain wall should grow exponentially to prevent annihilation at the domain boundaries. Though there is a classical result obtained by Basu and Vilenkin that the width of the wall tends to the one of the stationary solution (constant physical width). That is why we considered thick domain walls in a de Sitter universe following paper by Basu and Vilenkin However, we were interested not only in stationary solutions found therein, but also investigated the general case of domain wall evolution with time. When the wall thickness parameter, delta(0), is smaller than H-1/ root 2, where H is the Hubble parameter in de Sitter space-time, then the stationary solutions exist, and initial field configurations tend with time to the stationary ones. However, there are no stationary solutions for delta(0) >> H-1/ V. We have calculated numerically the rate of the wall expansion in this case and have found that the width of the wall grows exponentially fast for H-`. An explanation for the critical value = H-1/ Vr2 is also proposed.