Probing dark photons in the early universe with big bang nucleosynthesis

We perform calculations of dark photon production and decay in the early universe for ranges of dark photon masses and vacuum coupling with standard model photons. Simultaneously and self-consistently with dark photon production and decay, our calculations include a complete treatment of weak decoupling and big bang nucleosynthesis (BBN) physics. These calculations incorporate all relevant weak, electromagnetic, and strong nuclear reactions, including charge-changing (isospin-changing) lepton capture and decay processes. They reveal a rich interplay of dark photon production, decay, and associated out-of-equilibrium transport of entropy into the decoupling neutrino seas. Most importantly, the self-consistent nature of our simulations allows us to capture the magnitude and phasing of entropy injection and dilution. Entropy injection-induced alteration of the time-temperature-scale factor relation during weak decoupling and BBN leads to changes in the light element abundance yields and the total radiation content (as parametrized by $N_{\rm eff}$). These changes suggest ways to extend previous dark photon BBN constraints. However, our calculations also identify ranges of dark photon mass and couplings not yet constrained, but perhaps accessible and probable, in future Stage-4 cosmic microwave background experiments and future high precision primordial deuterium abundance measurements.