Dark matter as the signal of grand unification

We argue that the existence of dark matter (DM) is a possible consequence of grand unification (GUT) symmetry breaking. In GUTs like $SO(10)$, discrete Z₂ matter parity (-1)^3(B-L) survives despite broken B-L, and group theory uniquely determines that the only possible Z₂-odd matter multiplets belong to representation 16. We construct the minimal nonsupersymmetric $SO(10)$ model containing one scalar 16 for DM and study its predictions below MG. We find that electroweak symmetry breaking occurs radiatively due to DM couplings to the standard model Higgs boson. For thermal relic DM the mass range MDM~O(0.1--1) TeV is predicted by model perturbativity up to MG. For MDM~O(1) TeV to explain the observed cosmic ray anomalies with DM decays, there exists a lower bound on the spin-independent direct detection cross section within the reach of planned experiments.