Dark Photon, CMB and radio data in our inhomogeneous universe

The dark photon is a well-motivated extension of the Standard Model which can mix with the regular photon. Whenever the dark photon mass matches the photon plasma frequency, a resonant conversion between photons and dark photons is possible. These conversions can produce observable cosmological signatures, including distortions to the cosmic radiation background. In this talk, I will discuss a new analytic formalism for these conversions that can account for the inhomogeneous distribution of matter in our universe, leading to new limits on the mixing parameter of light dark photons using COBE/FIRAS measurement of the cosmic microwave background spectrum. I will also briefly describe how a simple dark sector can explain the longstanding ARCADE radio background excess through resonant conversions of dark photons.