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We show how gauge coupling unification is successfully implemented throughnon-supersymmetric grand unified theory, $SO(10)\times G_f (~G_f=S_4, SO(3)_f,SU(3)_f)$, using low-scale flavor symmetric model of the type $SU(2)_L\timesU(1)_Y$ $ \times SU(3)_C \times S_4$ recently proposed by Hagedorn, Lindner,and Mohapatra, while assigning matter-parity discrete symmetry for the darkmatter stability. For gauge coupling unification in the single-step breakingcase, we show that a color-octet fermion and a hyperchargeless weak-tripletfermionic dark matter are the missing particles needed to complete itsMSSM-equivalent degrees of freedom. When these are included the modelautomatically predicts the nonsupersymmetric grand unification with a scaleidentical to the minimal supersymmetric standard model/grand unified theoryscale. We also find a two-step breaking model with Pati-Salam intermediatesymmetry where the dark matter and a low-mass color-octet scalar or the fermionare signaled by grand unification. The proton-lifetime predictions are found tobe accessible to ongoing or planned searches in a number of models. We discussgrand unified origin of the light fermionic triplet dark matter, thecolor-octet fermion, and their phenomenology.

Flavor unification, dark matter, proton decay and other observable predictions with low-scale $S_4$ symmetry