Dark Matter and Electroweak Symmetry Breaking from $SO(10)$

We consider a minimal model of GUT scalar dark matter (DM) stabilized by the discrete gauge matter parity $P_{X}$ that arises from breaking of $SO(10)$. The dark sector comprises the complex singlet $S$ and the inert doublet $H_{2}$. GUT scale parameters are evaluated to the electroweak scale via Renormalization Group Equations (RGEs). Experimental and theoretical constraints limit the DM mass to the 80 GeV to 2 TeV range. The EW symmetry breaking is radiative and can occur via RGE running and 1-loop matching corrections from integrating out DM. Because the next-to-lightest scalar is almost degenerate with DM, it gives a background free displaced decay vertex at the LHC.