We consider a simple abelian vector dark matter (DM) model, where {it only} the DM $(widetilde{X}_mu)$ couples non-minimally to the scalar curvature $(widetilde{R})$ of the background spacetime via an operator of the form $sim widetilde{X}_mu,widetilde{X}^mu,widetilde{R}$. By considering the standard freeze-out scenario, we show, it is possible to probe such a non-minimally coupled DM in direct detection experiments for a coupling strength $xisimmathcal{O}left(10^{30}right)$ and DM mass $m_Xlesssim 55$ TeV, satisfying Planck observed relic abundance and perturbative unitarity. We also discuss DM production via freeze-in, governed by the non-minimal coupling, that requires $xilesssim 10^5$ to produce the observed DM abundance over a large range of DM mass depending on the choice of the reheating temperature. We further show, even in the absence of the non-minimal coupling, it is possible to produce the whole observed DM abundance via 2-to-2 scattering of the bath particles mediated by massless gravitons.
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