Neutralino relic density in a Universe with non-vanishing cosmological constant

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 such limits read as: $M_{1/2} \simeq 300 \GeV - 340 \GeV$, $m_0 \simeq 80 \GeV - 130 \GeV$. A way to avoid these stringent 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.