  We study the quantum effects induced by bulk scalar fields in a model with a
de Sitter (dS) brane in a flat bulk (the Vilenkin-Ipser-Sikivie model) in more
than four dimensions. In ordinary dS space, it is well known that the stress
tensor in the dS invariant vacuum for an effectively massless scalar
($m_\eff^2=m^2+\xi {\cal R}=0$ with ${\cal R}$ the Ricci scalar) is infrared
divergent except for the minimally coupled case. The usual procedure to tame
this divergence is to replace the dS invariant vacuum by the Allen Follaci (AF)
vacuum. The resulting stress tensor breaks dS symmetry but is regular.
Similarly, in the brane world context, we find that the dS invariant vacuum
generates $\tmn$ divergent everywhere when the lowest lying mode becomes
massless except for massless minimal coupling case. A simple extension of the
AF vacuum to the present case avoids this global divergence, but $\tmn$ remains
to be divergent along a timelike axis in the bulk. In this case, singularities
also appear along the light cone emanating from the origin in the bulk,
although they are so mild that $\tmn$ stays finite except for non-minimal
coupling cases in four or six dimensions. We discuss implications of these
results for bulk inflaton models. We also study the evolution of the field
perturbations in dS brane world. We find that perturbations grow linearly with
time on the brane, as in the case of ordinary dS space. In the bulk, they are
asymptotically bounded.
