Vector dark matter, inflation and non-minimal couplings with gravity

We propose a cosmological dark matter production mechanism in the form of a longitudinal massive vector boson. We build upon the work of Graham et.al. including non-minimal couplings of the massive vector with gravity, developing a well motivated set-up from an effective field theory perspective. We carefully track the dynamics of vector field in passing from inflation to radiation dominated universe to show that the late time abundance of longitudinal modes -- excited initially by the quantum fluctuations during inflation -- can provide the observed dark matter abundance for sufficiently weak non-minimal coupling and wide range of vector masses $5 \times 10^{-7} \lesssim m\, [{\rm eV}] \lesssim 5 \times 10^{3}$. The final abundance of dark matter depends on two parameter, the vector mass and its non-minimal coupling with gravity. We discuss experimental venues to probe this framework, including the production of a stochastic gravitational wave background. The latter is especially interesting, as the same mechanism that generates dark matter can potentially lead to the production of gravitational waves in the LISA frequency band, through the second-order effects of large dark matter iso-curvature perturbations at small scales. We take a first step in this direction, identifying the potential information that gravitational wave experiments can provide on the parameter space of dark matter within this scenario.