Adding matter to Poincaré invariant branes

A solution to the cosmological constant problem has been proposed in which our universe is a 3-brane in a 5-dimensional spacetime. With a bulk scalar, the field equations admit a Poincare invariant brane solution regardless of the value of the cosmological constant (tension) on the brane. However, the solution does not include matter in the brane. We find new exact static solutions with matter density and pressure in the brane. We study small perturbations about these solutions. None seem consistent with observational cosmology. As a by-product we find a class of new matterless static solutions and a non-static solution which, curiously, requires the string value for the dilaton coupling.