  In the previous works (arXiv:1202.5375 and 1402.1346), the dynamical domain
wall, where the four dimensional FRW universe is embedded in the five
imensional space-time, has been realized by using two scalar fields. In this
paper, we consider the localization of vector field in three formulations. The
first formulation was investigated in the previous paper (arXiv:1510.01099) for
the $U(1)$ gauge field. In the second formulation, we investigate the
Dvali-Shifman mechanism (hep-th/9612128), where the non-abelian gauge field is
confined in the bulk but the gauge symmetry is spontaneously broken on the
domain wall. In the third formulation, we investigate the Kaluza-Klein modes
coming from the five dimensional graviton. In the Randall-Sundrum model, the
graviton was localized on the brane. We show that the $(5,\mu)$ components
$\left(\mu=0,1,2,3\right)$ of the graviton are also localized on the domain
wall and can be regarded as the vector field on the domain wall. There are,
however, some corrections coming from the bulk extra dimension if the domain
wall universe is expanding.
