Dark radiation from inflationary fluctuations

Light new vector bosons can be produced gravitationally through quantum fluctuations during inflation; if these particles are feebly coupled and cosmologically metastable, they can account for the observed dark matter abundance. However, in minimal anomaly-free $U(1)$ extensions to the Standard Model, these vectors generically decay to neutrinos if at least one neutrino mass eigenstate is sufficiently light. If these decays occur between neutrino decoupling and cosmic microwave background (CMB) freeze-out, the resulting radiation energy density can contribute to $ΔN_{eff}$ at levels that can ameliorate the Hubble tension and be discovered with future CMB and relic neutrino detection experiments. Since the additional neutrinos are produced from vector decays after Big Bang Nucleosynthesis (BBN), this scenario predicts $ΔN_{eff}>0$ at recombination, but $ΔN_{eff}=0$ during BBN. Furthermore, due to a fortuitous cancellation, the contribution to $ΔN_{eff}$ is approximately mass independent.