  We explore a mechanism to produce a light dark photon dark matter through a
coupling between the dark photon field and a spectator scalar field which plays
no role in the inflationary expansion of the Universe while rolling down its
potential during the inflation. The motion of the spectator field efficiently
produces dark photons with large wavelengths which become non-relativistic
before the time of matter-radiation equality. The spectrum of the wavelengths
is peaky so that the constraint from the isocurvature perturbation can be
evaded. The correct relic abundance is then achieved over a wide range of the
dark photon mass down to $10^{-13} \ \text{eV}$. Our mechanism favors
high-scale inflation models which can be tested in future observations.
Furthermore, fluctuations of the dark photon field during inflation produce
gravitational waves detectable at future space-based interferometers and/or
pulsar timing array experiments.
