  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.
