  In the framework of the Constrained Minimal Supersmmetric Standard Model
(CMSSM) we discuss the impact of the pseudo-scalar Higgs boson in delineating
regions of the parameters which are consistent with cosmological data and E821
data on the anomalous magnetic moment of muon. For large values of the
parameter $\tan \beta > 50$, cosmologically allowed corridors of large $m_0$,
$M_{1/2}$ are opened, due to the s-channel pseudo-scalar exchange in the pair
annihilation of the lightest of the neutralinos to $b \bar{b}$ or $\tau
\bar{\tau}$, which dominates in this region. However, no such corridors are
found for values $\tan \beta < 50 $. Combining cosmological and E821 data puts
severe upper limits on sparticle masses. We find that at LHC, but even at a
$e^{+}e^{-}$ linear collider with center of mass energy $\sqrt{s} = 800\GeV$,
such as TESLA, supersymmetry can be discovered, if it is based on the CMSSM.
