Domain walls, stabilities, and the mass hierarchy of the Randall-Sundrum Model

Randall-Sundrum model, which has a scalar field, is used to investigate the domain structure of the extra dimension and to obtain a possible solution of the mass hierarchy problem. It is found that when the domain wall size is comparable to that of domains, domains become unstable. To construct a reliable theory, a region of physical parameter space, where domains are stable, is identified. Analytic forms of field configurations are obtained by perturbative expansions in term of a small parameter that is approximately equal to the relative size of domain wall with respect to domains. By placing a single 3-brane in one of the domain, one can solve the mass hierarchy problem.