Supersymmetric dark matter above the $W$ mass

In this paper we study the cosmological consequences of the minimal supersymmetric extension of the standard model in the case that the neutralino is heavier than the $W$. We calculate the cross section for annihilation of heavy neutralinos into final states containing gauge and Higgs bosons ($\tilde{\chi }\tilde{\chi }\to WW,ZZ,HH,HW,HZ$) and combine these results with those previously obtained for annihilation into fermions to find the relic cosmological abundance for the most general neutralino. The new channels are particularly important for Higgsino-like and mixed-state neutralinos, but are subdominant (to the fermion-antifermion annihilation channels) in the case that the neutralino is mostly a gaugino. The effect of the top-quark mass is also considered. Using these cross sections and the cosmological constraint ${\Omega }_{\tilde{\chi }}{h}^2\lesssim 1$ we map the entire range of cosmologically acceptable supersymmetric parameter space and find a very general bound on the neutralino mass. For a top-quark mass of less than 180 GeV, neutralinos heavier than 3200 GeV are cosmologically inconsistent, and if the top-quark mass is less than 120 GeV, the bound is lowered to 2600 GeV. We find that a "heavy" neutralino ($m_{\tilde{\chi }}>m_W$) that contributes ${\Omega }_{\tilde{\chi }}\sim 1$ arises for a very wide range of model parameters and makes, therefore, a very natural and attractive dark-matter candidate.