  We examine supergravity models with grand unification at M_G possessing R
parity invariance. Current data has begun to significantly constrain the
parameter space. Thus for mSUGRA, accelerator data places a lower bound on
m_{1/2} of m_{1/2} >~300 GeV while astronomical data on the amount of relic
dark matter narrowly determines m_0 in terms of m_{1/2} (for fixed value of
tanbeta and A_0) due to co-annihilation effects. Additional new data could fix
the parameters further. Thus the parameter space is sensitive to the muon
magnetic moment anomaly, \delta a_\mu, and if \delta a_\mu lies 1 \sigma above
its current central value, it would exclude mSUGRA, while if it lies 1\sigma
below (but is still positive) it pushes the SUSY spectrum into the TeV domain.
The B_s ->\mu^+ \mu^- decay is seen to be accessible to the Tevatron RunII with
branching ratio sensitivity of Br[B_s ->\mu^+ \mu^-] > 6.5\times10^{-9} with 15
fb^{-1}/detector, and a value of 7(14)\times10^{-8} obtainable with 2 fb^{-1}
would be sufficient to exclude mSUGRA for tan beta < 50(55). Measurements of
B_s ->\mu^+ \mu^- can cover the full mSUGRA parameter space for tanbeta > 40 if
\delta a_\mu > 11\times10^{-10}, and combined measurements of B_s -> \mu^+
\mu^-, a_\mu and m_h (or alternately the gluino mass) would effectively
determine the mSUGRA parameters for \mu > 0. Detector cross sections are then
within the range of planned future dark matter experiments. Non-universal
models are also discussed, and it is seen that detector cross sections there
can be much larger, and can be in the DAMA data region.
