  We study the consequences of the gravitino decay into dark matter. We suppose
that the lightest neutralino is the main component of dark matter. In our
framework gravitino is heavy enough to decay before Big Bang Nucleosynthesis
starts. We consider a model coming from a five dimensional supergravity
compactified on $S^1/Z_2$ with gravity in the bulk and matter localized on
tensionless branes at the orbifold fixed points. We require that the dark
matter, which is produced thermally and in the decay of Kaluza-Klein modes of
gravitino, has an abundance compatible with observation. We deduce from our
model that there are curves of constraints between the size of the
extra-dimension and the reheating temperature of the universe after inflation.
This talk is based on hep-ph/0702183 to be published in \PRD.
