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Constraints on hidden photons from current and future observations of CMB spectral distortions

A variety of beyond the standard model scenarios contain very light hidden sector U(1) gauge bosons undergoing kinetic mixing with the photon. The resulting oscillation between ordinary and hidden photons leads to spectral distortions of the cosmic microwave background. We update the bounds on the mixing parameter $χ_0$ and the mass of the hidden photon $m_{γ'}$ for future experiments measuring CMB spectral distortions, such as PIXIE and PRISM/COrE. For $10^{-14}\;{\rm eV}\lesssim m_{γ'}\lesssim 10^{-13}\;{\rm eV}$, we find the kinetic mixing angle $χ_0$ has to be less than $10^{-8}$ at 95\% CL. These bounds are more than an order of magnitude stronger than those derived from the COBE/FIRAS data.