Neutralino Dark Matter Elastic Scattering in a Flat and Accelerating Universe

In SUGRA inspired supersymmetric models with universal boundary conditions for the soft masses, the scalar cross section $\sigma_{scalar}$ for the elastic neutralino--nucleon scattering is in general several orders of magnitude below the sensitivity of current experiments. For large $\tan \beta$ and low $M_{1/2}, m_0$ values, the theoretically predicted $\sigma_{scalar}$ can approach the sensitivity of these experiments ($\approx 10^{-6} pb$) being at the same time in agreement with recent cosmological data, which impose severe restrictions on the CDM relic density, and with accelerator experiments which put lower bounds on sparticle and Higgs boson masses. Further improvement of the sensitivity of DAMA and CDMS experiments will probe the large $\tan \beta$ region of the parameter space in the vicinity of the boundaries of the parameter space allowed by chargino and Higgs searches.