Dark Photon Dark Matter from Quantum Fluctuations during Starobinsky Inflation

We present a detailed investigation of scenarios in which dark-photon dark matter is produced from quantum fluctuations during inflation. In particular, we focus on inflationary models that necessarily involve a Weyl transformation, dependent on the inflaton amplitude, in order to move to the Einstein frame. In such models, the kinetic function of the longitudinal mode of the dark photon varies throughout, and even after, the inflationary period. We show that this variation of the kinetic function has a substantial impact on the resulting relic abundance of dark photons. As a representative and phenomenologically important example, we analyze the Starobinsky inflation model, for which we perform an accurate computation of the relic dark-photon abundance. By imposing the relevant observational constraints, we find that, in order to reproduce the observed dark-matter density in the present Universe, the dark-photon mass must lie in the range 5.6 < m < 7.4, mu eV within the framework considered in this work.