  We highlight some universal features concerning the role of spacetime
curvature in the entanglement induced between quantum probes coupled to a
quantum field in a suitable vacuum state. The probes are initially causally
disconnected and non-entangled. We explore the parameter space $\{{\omega},
d_0, \boldsymbol{v}_0\}$ spanned by the energy gap $\omega$ of the detectors,
and the initial values of separation distance $d_0$ and relative velocity
$\boldsymbol{v}_0$, both covariantly defined in arbitrary curved spacetime. We
also obtain numerical results in de Sitter spacetimes and use these to explore
strong curvature regime, while also corroborating our perturbative results in
arbitrary curved spacetime. Our analysis shows that curvature can induce
entanglement features in certain regions of the above parameter space, in a
manner which facilitates using entanglement as a probe of spacetime curvature.
