Light and Feebly Interacting Non-Abelian Vector Dark Matter Produced Through Vector Misalignment

In this paper, we examine the evolution of light and feebly interacting non-abelian dark gauge bosons dark matter in the early universe. We specifically work on a multi-component dark matter scenario with a $SU(2)_{_R}$ gauge symmetry, spontaneously broken by a scalar $\phi$. For sufficiently light $\lesssim O( \rm{MeV})$ and feebly interacting $(g_{_R} \lesssim 10^{-10})$ gauge bosons, $W^3_{_R}$ and $W^{\pm}_{_R} \equiv W_{_R}^1 \pm i W_{_R}^2$ become the dark matter candidates. In this study, the portal between the dark sector and the standard model sector is provided by the right-handed electron charged under $SU(2)_{_R}$. We show that in the region of the parameter space where $g_{_R} \sim 10^{-12}$, the dark gauge boson $W^3_{_R}$ can be produced efficiently via the freeze-in mechanism, however, this mechanism fails to produce $W^{\pm}_{_R}$ sufficiently. For smaller dark gauge coupling, the relic density of three dark matter components can be obtained via the vector misalignment mechanism. Vector misalignment has already been discussed in the case of dark photon dark matter. In this study, we extend the arguments to non-abelian gauge bosons. After discussing the evolution of $W_{_R}$s in the early universe, we study the model's constraints and show the parameter space's allowed region.