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A first order dark $SU(2)_D$ phase transition with vector dark matter in the light of NANOGrav 12.5 yr data

We study a dark $SU(2)_D$ gauge extension of the standard model (SM) with the possibility of a strong first order phase transition (FOPT) taking place below the electroweak scale in the light of NANOGrav 12.5 yr data. As pointed out recently by the NANOGrav collaboration, gravitational waves (GW) from such a FOPT with appropriate strength and nucleation temperature can explain their 12.5 yr data. We impose a classical conformal invariance on the scalar potential of $SU(2)_D$ sector involving only a complex scalar doublet with negligible couplings with the SM Higgs. While a FOPT at sub-GeV temperatures can give rise to stochastic GW around nano-Hz frequencies being in agreement with NANOGrav findings, the $SU(2)_D$ vector bosons which acquire masses as a result of the FOPT in dark sector, can also serve as dark matter (DM) in the universe. The relic abundance of such vector DM can be generated in a non-thermal manner from the SM bath via scalar portal mixing. We also discuss future sensitivity of gravitational wave experiments to the model parameter space.