  We discuss the relic density of the lightest of the supersymmetric particles
in view of new cosmological data, which favour the concept of an accelerating
Universe with a non-vanishing cosmological constant. Recent astrophysical
observations provide us with very precise values of the relevant cosmological
parameters. Certain of these parameters have direct implications on particle
physics, e.g., the value of matter density, which in conjunction with
electroweak precision data put severe constraints on the supersymmetry breaking
scale. In the context of the Constrained Minimal Supersymmetric Standard Model
(CMSSM) such limits read as: $M_{1/2} \simeq 300 \GeV - 340 \GeV$, $m_0 \simeq
80 \GeV - 130 \GeV$. Within the context of the CMSSM a way to avoid these
constraints is either to go to the large $\tan \beta$ and $\mu > 0$ region, or
make ${\tilde \tau}_R$, the next to lightest supersymmetric particle (LSP), be
almost degenerate in mass with LSP.
