  While a wide variety of astrophysical and cosmological phenomena suggest the
presence of Dark Matter, all evidence remains via its gravitational effect on
the known matter. As such, it is conceivable that this evidence could be
explained by a modification to gravitation and/or concepts of inertia. Various
formulations of modified gravity exist, each giving rise to several
non-canonical outcomes. This motivates us to propose an experiment searching
for departures from (quantum) Newtonian predictions in a bipartite setting with
gravitational accelerations $\lesssim 10^{-10}$ m/s$^2$, i.e., where the
effective force needs to be stronger than Newtonian to account for the Dark
Matter effects. Since quantum particles naturally source weak gravitation,
their non-relativistic dynamics offers opportunities to test this small
acceleration regime. We show that two nearby mesoscopic quantum masses
accumulate significantly larger entanglement in modified gravity models, such
as the Modified Newtonian Dynamics. Our calculations include Casimir-Polder
forces as well as tidal effects next to the surface of the earth, and confirm
that entanglement is observable within the limits imposed by environmental
decoherence. We demonstrate how the temperature can be fine-tuned such that
modified gravity is certified simply by witnessing the entanglement generated
from uncorrelated thermal states, eliminating the need for precise noise
characterization. Overall, the required parameters could be realized in a
tabletop experiment.
