  We discuss the bulk Casimir effect (effective potential) for a conformal or
massive scalar when the bulk represents five-dimensional AdS or dS space with
two or one four-dimensional dS brane, which may correspond to our universe.
Using zeta-regularization, the interesting conclusion is reached, that for both
bulks in the one-brane limit the effective potential corresponding to the
massive or to the conformal scalar is zero. The radion potential in the
presence of quantum corrections is found. It is demonstrated that both the dS
and the AdS braneworlds may be stabilized by using the Casimir force only. A
brief study indicates that bulk quantum effects are relevant for brane
cosmology, because they do deform the de Sitter brane. They may also provide a
natural mechanism yielding a decrease of the four-dimensional cosmological
constant on the physical brane of the two-brane configuration.
