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 CMB freeze out, the resulting radiation energy density can contribute to $\Delta N_{\rm eff}$ 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 BBN, this scenario predicts $\Delta N_{\rm eff} > 0$ at recombination, but $\Delta N_{\rm eff} = 0$ during BBN. Furthermore, due to a fortuitous cancellation, the contribution to $\Delta N_{\rm eff}$ is approximately mass independent.