We re-examine the parameter space of the constrained minimal supersymmetric extension of the Standard Model (CMSSM), taking account of the restricted range of Ω CDM h 2 consistent with the WMAP data. This provides a significantly reduced upper limit on the mass of the lightest supersymmetric particle LSP: m χ < ∼ 500 GeV for tan β < ∼ 45 and µ > 0, or tan β < ∼ 30 and µ < 0, thereby improving the prospects for measuring supersymmetry at the LHC, and increasing the likelihood that a 1-TeV linear e + e − collider would be able to measure the properties of some supersymmetric particles.

If the gravitino is the lightest supersymmetric particle and the long-lived next-to-lightest sparticle (NSP) is the stau, the charged partner of the tau lepton, it may be metastable and form bound states with several nuclei. These bound states may affect the cosmological abundances of 6 Li and 7 Li by enhancing nuclear rates that would otherwise be strongly suppressed. We consider the effects of these enhanced rates on the final abundances produced in Big-Bang nucleosynthesis (BBN), including injections of both electromagnetic and hadronic energy during and after BBN. We calculate the dominant two-and three-body decays of both neutralino and stau NSPs, and model the electromagnetic and hadronic decay products using the PYTHIA event generator and a cascade equation. Generically, the introduction of bound states drives light element abundances further from their observed values; however, for small regions of parameter space bound state effects can bring lithium abundances in particular in better accord with observations. We show that in regions where the stau is the NSP with a lifetime longer than 10 3 − 10 4 s, the abundances of 6 Li and 7 Li are far in excess of those allowed by observations. For shorter lifetimes of order 1000 s, we comment on the possibility in minimal supersymmetric and supergravity models that stau decays could reduce the 7 Li abundance from standard BBN values while at the same time enhancing the 6 Li abundance.

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

We consider the possibility that the gravitino might be the lightest supersymmetric particle (LSP) in the constrained minimal extension of the Standard Model (CMSSM). In this case, the next-to-lightest supersymmetric particle (NSP) would be unstable, with an abundance constrained by the concordance between the observed light-element abundances and those calculated on the basis of the baryon-to-entropy ratio determined using CMB data. We modify and extend previous CMSSM relic neutralino calculations to evaluate the NSP density, also in the case that the NSP is the lighter stau, and show that the constraint from late NSP decays is respected only in a limited region of the CMSSM parameter space. In this region, gravitinos might constitute the dark matter.