Supersymmetry spectrum constraints and direct dark matter detection

We perform an investigation of the minmal supersymmetric standard model (MSSM) parameter space at the Fermi scale taking into account available accelerator, nonaccelerator and cosmological constraints. Extra assumptions about upper bounds for some of the supersymmetry (SUSY) particles are also imposed. We show that a nonobservation of the SUSY dark matter candidates with a high-accuracy dark matter detector, such as ${}^{73}\mathrm{Ge},$ under the above-mentioned assumptions can exclude large domains of the MSSM parameter space and, for instance, can make especially desirable the collider search for a light SUSY charged Higgs boson.