Fermion masses in SO(10)

Yukawa-coupling-constant unification together with the known fermion masses is used to constrain SO(10) models. We consider the case of one (heavy) generation, with the tree-level relation $m_b=m_{\tau }$, calculating the limits on the intermediate scales due to the known limits on fermion masses. This analysis extends previous analyses which addressed only the simplest symmetry-breaking schemes. In the case where the low-energy model is the standard model with one Higgs doublet, there are very strong constraints due to the known limits on the top-quark mass and the $\tau$-neutrino mass. The two-Higgs-doublet case is less constrained, though we can make progress in constraining this model also. We identify those parameters to which the viability of the model is most sensitive. We also discuss the "triviality" bounds on $m_t$ obtained from the analysis of the Yukawa renormalization-group equations. Finally we address the role of a speculative constraint on the $\tau$-neutrino mass, arising from the cosmological implications of anomalous $B+L$ violation in the early Universe.