  We investigate the so-called superWIMP scenario with gravitino as the
lightest supersymmetric particle (LSP) in the context of non-standard
cosmology, in particular, brane world cosmology. As a candidate of the
next-to-LSP (NLSP), we examine slepton and sneutrino. Brane world cosmological
effects dramatically enhance the relic density of the slepton or sneutrino
NLSP, so that the NLSP with mass of order 100 GeV can provide the correct
abundance of gravitino dark matter through its decay. We find that with an
appropriate five dimensional Planck mass, this scenario can be realized
consistently with the constraints from Big Bang Nucleosynthesis (BBN) for both
NLSP candidates of slepton and sneutrino. The BBN constraints for slepton NLSP
are more stringent than that for sneutrino, as the result, the gravitino must
be rather warm in the slepton NLSP case. The energy density of gravitino
produced by thermal scattering is highly suppressed and negligible due to the
brane world cosmological effects.
