ar X iv : h ep - p h / 04 04 26 6 v 1 29 A pr 2 00 4 YUKAWA QUASI - UNIFICATION AND INFLATION

We review the construction of a concrete supersymmetric grand unified model, which naturally leads to a moderate violation of ‘asymptotic’ Yukawa unification and, thus, can allow an acceptable b-quark mass within the constrained minimal supersymmetric standard model with μ > 0. The model possesses a wide and natural range of parameters which is consistent with the data on the cold dark matter abundance in the universe, b → sγ, the muon anomalous magnetic moment and the Higgs boson masses. Also, it automatically leads to a new version of shifted hybrid inflation, which avoids overproduction of monopoles at the end of inflation by using only renormalizable terms.