  We study brane cosmology as 4D (4-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
non-trivial 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.
