Yukawa Quasi-Unification and Neutralino Relic Density

The construction of a Supersymmetric Grand Unified Model based on the Pati-Salam gauge group is briefly reviewed and the low energy consequences of the derived asymptotic Yukawa quasi-unification conditions are examined. In the framework of the resulting Constrained Minimal Supersymmetric Standard Model, the cosmological relic density of the bino-like LSP is calculated and the results are explicitly compared with {\tt micrOMEGAs}. In addition to the Cold Dark Matter constraint, restrictions on the parameter space, arising from the Higgs boson masses, the SUSY corrections to $b$-quark mass, the muon anomalous magnetic moment and the inclusive decay $b\to s\gamma$ are, also, investigated. For $\mu>0$, a wide and natural range of parameters is allowed. On the contrary, the $\mu<0$ case not only is disfavored from the present experimental data on the muon anomalous magnetic moment, but also, it can be excluded from the combination of the Cold Dark Matter and BR($b\to s \gamma$) requirements.