Neutralino Dark Matter in MSSM Models with Non-Universal Higgs Masses

We consider the Minimal Supersymmetric Standard Model (MSSM) with varying amounts of non-universality in the soft supersymmetry-breaking contributions to the Higgs scalar masses. In addition to the constrained MSSM (CMSSM) in which these are universal with the soft supersymmetry-breaking contributions to the squark and slepton masses at the input GUT scale, we consider scenarios in which both the Higgs masses are non-universal by the same amount (NUHM1), and scenarios in which they are independently non-universal (NUHM2). As the lightest neutralino is a dark matter candidate, we demand that the relic density of neutralinos not be in conflict with measurements by WMAP and others, and examine the viable regions of parameter space. Prospects for direct detection of neutralino dark matter via elastic scattering in these scenarios are discussed.