Cosmological Constraints on Very Dark Photons
  We explore the cosmological consequences of kinetically mixed dark photons with a mass between 1 MeV and 10 GeV, and an effective electromagnetic fine structure constant as small as $10^{-38}$. We calculate the freeze-in abundance of these dark photons in the early Universe and explore the impact of late decays on BBN and the CMB. This leads to new constraints on the parameter space of mass $m_V$ vs kinetic mixing parameter $\kappa$. 
Anthony Fradette, Maxim Pospelov, Josef Pradler and Adam Ritz
hep-ph astro-ph.CO