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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 ≃ 300 GeV − 340 GeV, m 0 ≃ 80 GeV − 130 GeV. Within the context of the CMSSM a way to avoid these constraints is either to go to the large tan β and µ > 0 region, or makeτ R , the next to lightest supersymmetric particle (LSP), be almost degenerate in mass with LSP.Pacs numbers: 95.30. Cq, 12.60.Jv, 95.35.+d