Markov chain Monte Carlo exploration of minimal supergravity with implications for dark matter

We explore the full parameter space of Minimal Supergravity (mSUGRA), allowing all four continuous parameters (the scalar mass m(0), the gaugino mass m(1/2), the trilinear coupling A(0), and the ratio of Higgs vacuum expectation values tan beta) to vary freely. We apply current accelerator constraints on sparticle and Higgs masses, and on the b --> sgamma branching ratio, and discuss the impact of the constraints on g(mu) - 2. To study dark matter, we apply the WMAP constraint on the cold dark matter density. We develop Markov Chain Monte Carlo (MCMC) techniques to explore the parameter regions consistent with WMAP, finding them to be considerably superior to previously used methods for exploring supersymmetric parameter spaces. Finally, we study the reach of current and future direct detection experiments in light of the WMAP constraint.