Domain wall dynamics in brane world and nonsingular cosmological models

We study brane cosmology as 4D (four-dimensional) domain-wall dynamics in 5D bulk spacetime. For a generic 5D bulk with 3D maximal symmetry, we derive the equation of motion of a domain wall and find that it depends on mass function of the bulk spacetime, and the energy-momentum conservation in a domain wall is affected by a lapse function in the bulk. Especially, for a bulk spacetime with nontrivial lapse function, energy of matter field on the domain wall goes out or comes in from the bulk spacetime. Applying our result to the case with SU(2) gauge bulk field, we obtain a singularity-free universe in brane world scenario, that is, not only a big bang initial singularity of the brane is avoided but also a singularity in a 5D bulk does not exist.