Neutralino relic density in minimalN=1supergravity

We compute the cosmic relic (dark matter) density of the lightestsupersymmetric particle (LSP) in the framework of minimal $N=1$ Supergravitymodels with radiative breaking of the electroweak gauge symmetry. To this end,we re--calculate the cross sections for all possible annihilation processes fora general, mixed neutralino state with arbitrary mass. Our analysis includeseffects of all Yukawa couplings of third generation fermions, and allows for afairly general set of soft SUSY breaking parameters at the Planck scale. Wefind that a cosmologically interesting relic density emerges naturally overwide regions of parameter space. However, the requirement that relicneutralinos do not overclose the universe does not lead to upper bounds on SUSYbreaking parameters that are strictly valid for all combinations of parametersand of interest for existing or planned collider experiments; in particular,gluino and squark masses in excess of 5 TeV cannot strictly be excluded. On theother hand, in the ``generic'' case of a gaugino--like neutralino whoseannihilation cross sections are not ``accidentally'' enhanced by a nearby Higgsor $Z$ pole, all sparticles should lie within the reach of the proposed $pp$and $e^+e^-$ supercolliders. We also find that requiring the LSP to provide alldark matter predicted by inflationary models imposes a strict lower bound of 40GeV on the common scalar mass $m$ at the Planck scale, while the lightestsleptons would have to be heavierComment: 53 pages(8figs are not included), Latex file; DESY 92-101, SLAC-PUB-586