Neutralino relic density in minimalN=1supergravity

We compute the cosmic relic (dark-matter) density of the lightest supersymmetric particle (LSP) in the framework of minimal $N=1\mathrm{}$ supergravity models with radiative breaking of the electroweak gauge symmetry. To this end, we recalculate the cross sections for all possible annihilation processes for a general, mixed neutralino state with arbitrary mass. Our analysis includes effects of all Yukawa couplings of third-generation fermions, and allows for a fairly general set of soft supersymmetry- (SUSY-) breaking parameters at the Planck scale. We find that a cosmologically interesting relic density emerges naturally over wide regions of parameter space. However, the requirement that relic neutralinos do not overclose the Universe does not lead to upper bounds on SUSY-breaking parameters that are strictly valid for all combinations of parameters and of interest for existing or planned collider experiments; in particular, gluino and squark masses in excess of 5 TeV cannot strictly be excluded. On the other hand, in the "generic" case of a gauginolike neutralino whose annihilation cross sections are not "accidentally" enhanced by a nearby Higgs boson or $Z$ pole, all sparticles should lie within the reach of the proposed $\mathrm{pp}$ and $e^{+}{e}^{-}$ supercolliders. We also find that requiring the LSP to provide all dark matter predicted by inflationary models imposes a strict lower bound of 40 GeV on the common scalar mass $m$ at the Planck scale, while the lightest sleptons would have to be heavier than 100 GeV. Fortunately, a large relic neutralino density does not exclude the possibility that charginos, neutralinos, gluinos, and squarks are all within the reach of the CERN $e^{+}{e}^{-}$ collider LEP 200 and the Fermilab Tevatron.