WMAP dark matter constraints and Yukawa unification in supergravity models withCPphases

The compatibility of producing the observed amount of dark matter, as indicated by the Wilkinson Microwave Anisotropy Probe (WMAP) data, through the relic abundance of neutralinos with Yukawa unification and with the measured rate of $b\to s\gamma$ is analyzed in mSUGRA and extended SUGRA unified models with the inclusion of $CP$ phases. The $CP$ phases affect the analysis in several ways, e.g., through the threshold corrections to the $b$-quark mass, via their effects on the neutralino relic density and through the supersymmetry (SUSY) contribution to the $\mathrm{BR}(b\to s\gamma )$ which is sensitive to the $CP$ phases. We present some specific models with large SUSY phases, which can accommodate the fermion electric dipole moment constraints and give a neutralino relic density in agreement with observations as well as with the $b\mathrm{\text{−}}\tau$ unification constraint. The possibility of achieving WMAP relic density constraints with full Yukawa unification is also explored.