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We propose a pseudo-Goldstone boson dark matter (pGDM) particle in $SO(10)$grand unified theory (GUT). Due to its Goldstone nature, this pGDM evades thedirect DM detection experiments which, otherwise, severely constrain theparameter space of DM models. In $SO(10)$, the pGDM is embedded as a linearcombination of the Standard Model (SM) singlet scalars in ${\bf 16_H}$ and${\bf 126_H}$ representations. We consider two scenarios for the intermediateroute of $SO(10)$ symmetry breaking (SB) to the SM: $SU(5) \times U(1)_X$ andPati-Salam the $SU(4)_c \times SU(2)_L \times SU(2)_R$ (4-2-2) gauge groups.The vacuum expectation value of ${\bf 126_H}$, which triggers the breaking of$U(1)_X$ and 4-2-2 symmetry in the two scenarios, respectively, determines thepGDM lifetime whose astrophysical lower bound provides one of the moststringent constraints. For the 4-2-2 route to $SO(10)$, the successful SM gaugecoupling unification requires the 4-2-2 breaking scale to be ${\cal O}(10^{11})$ GeV, and most of the parameter space is excluded. For the $SU(5)\times U(1)_X$ route, on the other hand, the $U(1)_X$ breaking scale can besignificantly higher, and a wide range of the parameter space is allowed.Furthermore, the proton lifetime in the $SU(5)$ case is predicted to be $4.53\times 10^{34}$ years, which lies well within the sensitivity reach of theHyper-Kamiokande experiment. We also examine the constraints on the modelparameter space from the Large Hadron Collider and the indirect DM search byFermi-LAT and MAGIC experiments.

Pseudo-Goldstone Dark Matter in $SO(10)$