  We study dark matter for gaugino-mediated supersymmetry breaking and compact
dimensions of order the grand unification scale. Higgs fields are bulk fields,
and in general their masses differ from those of squarks and sleptons at the
unification scale. As a consequence, at different points in parameter space,
the gravitino, a neutralino or a scalar lepton can be the lightest (LSP) or
next-to-lightest (NLSP) superparticle. We investigate the constraints from
primordial nucleosynthesis on the different scenarios. While neutralino and
gravitino dark matter with a sneutrino NLSP are consistent for a wide range of
parameters, gravitino dark matter with a stau NLSP is strongly constrained.
