The direct detection of neutralino dark matter is analysed in general supergravity scenarios, where non-universal soft scalar and gaugino masses can be present. In particular, the theoretical predictions for the neutralino-nucleon cross section are studied and compared with the sensitivity of dark matter detectors. We take into account the most recent astrophysical and experimental constraints on the parameter space, including the current limit on B(Bs-> mu+ mu-). The latter puts severe limitations on the dark matter scattering cross section, ruling out most of the regions that would be within the reach of present experiments. We show how this constraint can be softened with the help of appropriate choices of non-universal parameters which increase the Higgsino composition of the lightest neutralino and minimise the chargino contribution to the b->s transition.
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