b-tau Unification with Gaugino and Sfermion Mass non Universality

In the context of a SUSY GUT inspired MSSM version, the low energy consequences of the asymptotic $b-\tau$ Yukawa coupling Unification are examined, under the assumption of universal or non-universal boundary conditions for the gaugino and sfermion masses. Gaugino non-universality is applied, so that the SUSY corrections to $b$-quark mass can be reconciled with the present experimental data on muon anomalous magnetic moment. Restrictions on the parameter space, originating from the Cold Dark Matter abundance in the universe, the inclusive branching ratio of $b\to s\gamma$ and the accelerator data are, also, investigated and the scalar neutralino-proton cross section is calculated. In the case of a bino-like LSP and universal boundary conditions for the sfermion masses, the constraints, arising from the Cold Dark Matter and ${\rm BR}(b \to s\gamma)$ can be simultaneously satisfied, mainly thanks to the $A$-pole effect or the neutralino-stau coannihilations. In addition, sfermion mass non-universality provides the possibility of new coannihilation phenomena (neutralino-sbottom or neutralino-tau sneutrino-stau), which facilitate the simultaneous satisfaction of all the above requirements. In both cases above, the neutralino abundance can essentially decrease for a W-ino or higgsino like LSP creating regions of parameter space with additional neutralino-chargino and/or heavier neutralino coannihilations. The neutralino-sbottom mass proximity significantly ameliorates the detectability of LSP.