Résumé
The requirement that the lightest neutralino $\tilde\chi_1^0$ has the right thermal relic density to explain all Dark Matter in the universe strongly constrains the parameter space of supersymmetric models in general, and of the mSUGRA model in particular. Recently improved calculations of the mass of the light CP-even Higgs boson $h$ present in this model, and the increased central value of the mass of the top quark, have re--opened the possibility that $2 \mlsp \lsim m_h$. In this "$h-$pole region'' the LSP annihilation cross section is enhanced by near-resonant $h$ exchange in the $s-$channel, reducing the relic density to acceptable values. We delineate the corresponding region of mSUGRA parameter space, and explore its phenomenology. In particular, we find strong upper bounds on the masses of the gluino, lighter chargino and LSP.