  The scalar mode describing the fluctuation of the 3-brane (the observable
universe) in a five-dimensional bulk spacetime compactified on a circle is
absorbed by the Kaluza-Klein U(1) gauge field, leading to a massive
brane-vector living on the 3-brane. The brane-vector can be responsible for
dark matter because it is odd under a $\mathrm{Z}_2$ symmetry, neutral under
the Standard Model (SM) symmetries, and couples extremely weak to the SM
particles due to its gravitational origin. Interestingly, the brane-vector dark
matter could leave particular imprints on the cosmic microwave background (CMB)
and the primordial gravitational waves. Hence, the precise measurements of the
CMB and the observations of the primordial gravitational waves generated during
the inflation can provide a potential way to probe the extra-dimensions and
branes which are the main ingredients of string/M theory.
