The effect of nonuniversal SUSY soft breaking on the predictions of da
rk matter-detector event rates are surveyed for supergravity models wi
th gravity-mediated soft breaking. For universal soft breaking in the
first two generations and tan beta less than or similar to 20, nonuniv
ersal effects can be characterized by four parameters (two for Higgs b
osons and two for third-generation squarks) in addition to those of th
e minimal supergravity (SUGRA) model (MSGM). These can increase or dec
rease event rates by a factor of 10-100 in the domain m(chi 1)(0) less
than or similar to 60 GeV (chi(1)(0) is the lightest neutralino) but
produce generally small effects at higher masses. The value of the top
mass and b --> s + gamma branching ratio eliminate a major part of th
e parameter space for mu < 0, causing event rates for mu < 0 to be a f
actor about 100 smaller than those for mu > 0. A correlation between l
arge (small) event rates and small (large) b --> s + gamma branching r
atio is observed. The effect of future satellite (MAP and PLANCK) prec
ision determinations of cosmological parameters on the predicted event
rates is examined for the examples of the Lambda CDM and vCDM models.
It is seen that these could sharpen the event-rate predictions and al
so restrict the allowed gaugino-mass ranges, thus affecting prediction
s for accelerator SUSY searches.