First-order framework and domain-wall/brane-cosmology correspondence

We address the possibility of finding domain wall solutions from cosmological solutions in brane cosmology. We find first-order equations for corresponding cosmology/domain wall solutions induced on 3-branes. The quadratic term of energy density in the induced Friedmann equation plays a non-standard role and we discuss the way the standard cosmological and domain wall models are recovered as the brane tension becomes large and show how they can be described by four-dimensional supergravity action in such a limit. Finally, we show that gravity on the 3-brane is locally localized as one moves away from the two-dimensional domain walls living on the brane.