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We study Dark Matter (DM) abundance in the framework of the extension of theStandard Model (SM) with an additional $U(1)_X$ gauge symmetry. One complexsinglet is included to break the $U(1)_X$ gauge symmetry, meanwhile one of thedoublets is considered inert to introduce a DM candidate. The stability of theDM candidate is analyzed with a continuous $U(1)_X$ gauge symmetry as well asdiscrete $Z_2$ symmetry. We find allowed regions for the free model parameterswhich are in agreement with the most up-to-date experimental results reportedby CMS and ATLAS collaborations, the upper limit on WIMP-nucleon cross sectionimposed by XENON1T collaboration and the upper limit on the productioncross-section of a $Z^{\prime}$ gauge boson times the branching ratio of the$Z^{\prime}$ boson decaying into $\ell^-\ell^+$. We also obtain allowed regionsfor the DM candidate mass from the relic density reported by the PLANCKcollaboration including light, intermediate and heavy masses; depending mainlyon two parameters of the scalar potential, $\lambda_{2x}$ and$\lambda_{345}=\lambda_3+\lambda_4+2\lambda_5$. We find that trough$pp\rightarrow \chi\chi \gamma$ production, it may only be possible for afuture hadron-hadron Circular Collider (FCC-hh) to be able to detect a DMcandidate within the range of masses 10-60 GeV.

Dark matter in Inert Doublet Model with one scalar singlet and $U(1)_X$ gauge symmetry