  The hidden sector U(1) vector bosons created from inflationary fluctuations
can be a substantial fraction of dark matter if their mass is around
$10^{-5}$eV. The creation mechanism makes the vector bosons' energy spectral
density $\rho_{cdm}/\Delta E$ very high. Therefore, the dark electric dipole
transition rate in atoms is boosted if the energy gap between atomic states
equals the mass of the vector bosons. By using the Zeeman effect, the energy
gap between the 2S state and the 2P state in hydrogen atoms or hydrogen like
ions can be tuned. The $2S$ state can be populated with electrons due to its
relatively long life, which is about $1/7$s. When the energy gap between the
semi-ground $2S$ state and the 2P state matches the mass of the cosmic vector
bosons, induced transitions occur and the 2P state subsequently decays into the
1S state. The $2P\to1S$ decay emitted Lyman-$\alpha$ photons can then be
registered. The choices of target atoms depend on the experimental facilities
and the mass ranges of the vector bosons. Because the mass of the vector boson
is connected to the inflation scale, the proposed experiment may provide a
probe to inflation.
