  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.
