  If gravity is fundamentally quantum, any two quantum particles must get
entangled with each other due to their mutual interaction through gravity. This
phenomenon, dubbed gravity-mediated entanglement, has led to recent efforts of
detecting perturbative quantum gravity in table-top experimental setups. In
this paper, we generalize this to imagine two idealized massive oscillators, in
their ground state, which get entangled due to gravity in an expanding
universe, and find that the curvature of the background spacetime leaves its
imprints on the resulting entanglement profile. Thus, detecting
gravity-mediated entanglement from cosmological observations will open up an
exciting new avenue of measuring the local expansion rate of the cosmos.
