  So far all evidences of dark matter (DM) come from astrophysical and
cosmological observations, due to gravitational interactions of the DM. It is
possible that the true DM particle in the universe joins gravitational
interactions only, but nothing else. Such a Gravitational DM (GDM) acts as a
weakly interacting massive particle (WIMP), which is conceptually simple and
attractive. In this work, we explore this direction by constructing the
simplest scalar GDM particle $\chi_s$. It is a $Z_2$ odd singlet under the
standard model (SM) gauge group, and naturally joins the unique dimension-4
interaction with Ricci curvature, $\xi_s \chi_s^2 R$, where $\xi_s$ is the
dimensionless nonminimal coupling. We demonstrate that this gravitational
interaction $\xi_s \chi_s^2 R$, together with Higgs-curvature nonminimal
coupling term $\xi_h H^\dag H R$, induces effective couplings between
$\chi_s^2$ and SM fields which can account for the observed DM thermal relic
abundance. We analyze the annihilation cross sections of GDM particles and
derive the viable parameter space for realizing the DM thermal relic density.
We further study the direct/indirect detections and the collider signatures of
such a scalar GDM. These turn out to be highly predictive and testable.
