  We model the universe as a 3-brane embedded in five dimensional spacetime
with N=2 supersymmetry. The presence of the scalar fields of the universal
hypermultiplet in the bulk results in a positive pressure effectively reducing
the value of the cosmological constant and thereby providing a possible answer
as to why the measured value of the cosmological constant is many orders of
magnitude smaller than predicted from the vacuum energy. The solution allows
for any number of parallel branes to exist and relates their cosmological
constants (as well as matter densities and radiation pressures) to the value of
the dilaton in the extra dimension. The results we find can be thought of as
first order approximations, satisfying supersymmetry breaking and the
Bogomol'nyi-Prasad-Sommerfield (BPS) conditions in the bulk only.
