Neutralino Dark Matter in Minimal Supergravity: Direct Detection vs. Collider Searches

We calculate expected event rates for direct detection of relic neutralinos as a function of parameter space of the minimal supergravity model. Numerical results are presented for the specific case of a $^{73}$Ge detector. We find significant detection rates ($R> 0.01$ events/kg/day) in regions of parameter space most favored by constraints from $B\to X_s\gamma$ and the cosmological relic density of neutralinos. The detection rates are especially large in regions of large $\tan\beta$, where many conventional signals for supersymmetry at collider experiments are difficult to detect. If the parameter $\tan\beta$ is large, then there is a significant probability that the first direct evidence for supersymmetry could come from direct detection experiments, rather than from collider searches for sparticles.