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.

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.

Without assuming that Higgs masses have the same values as other scalar masses at the input GUT scale, we combine constraints on the minimal supersymmetric extension of the Standard Model (MSSM) coming from the cold dark matter density with the limits from direct searches at accelerators such as LEP, indirect measurements such as b → sγ decay and the anomalous magnetic moment of the muon. The requirement that Higgs massessquared be positive at the GUT scale imposes important restrictions on the MSSM parameter space, as does the requirement that the LSP be neutral. We analyze the interplay of these constraints in the (µ, m A ), (µ, m 1/2 ), (m 1/2 , m 0 ) and (m A , tan β) planes. These exhibit new features not seen in the corresponding planes in the constrained MSSM in which universality is extended to Higgs masses.

We compare updated predictions for the elastic scattering of supersymmetric neutralino dark matter with the improved experimental upper limit recently published by Cryogenic Dark Matter Search (CDMS) II. We take into account the possibility that the -nucleon term may be somewhat larger than was previously considered plausible, as may be supported by the masses of exotic baryons reported recently. We also incorporate the new central value of m t , which affects indirectly constraints on the supersymmetric parameter space, for example, via calculations of the relic density. Even if a large value of is assumed, the CDMS II data currently exclude only small parts of the parameter space in the constrained minimal standard model (CMSSM) with universal soft supersymmetry-breaking Higgs, squark, and slepton masses. None of the previously proposed CMSSM benchmark scenarios is excluded for any value of , and the CDMS II data do not impinge on the domains of the CMSSM parameter space favored at the 90% confidence level in a recent likelihood analysis. However, some models with nonuniversal Higgs, squark, and slepton masses and neutralino masses & 700 GeV are excluded by the CDMS II data.