Constraints on brane and bulk ideal fluid in Randall-Sundrum cosmologies

We investigate constraints for including bulk and brane matter in the Randall- Sundrum model. In the static configuration with two zero thickness branes, we find that no realistic brane matter is possible when the radion is stabilized. We also consider the possibility that the radion has stabilized by dissipating its energy into the bulk in the form of some unspecified matter, and find the Randall-Sundrum cosmological solutions in the presence of bulk ideal fluid. We discover that there is only one allowed equation of state, $p=\rho $, corresponding to the stiff ideal fluid. We find the corresponding brane cosmologies and compare them with the Friedmann-Robertson- Walker model.