  We consider the Standard Model extended with a dark matter particle in curved
spacetime, motivated by the fact that the only current evidence for dark matter
is through its gravitational interactions, and we investigate the impact on the
dark matter stability of terms in the Lagrangian linear in the dark matter
field and proportional to the Ricci scalar. We show that this "gravity portal"
induces decay even if the dark matter particle only has gravitational
interactions, and that the decay branching ratios into Standard Model particles
only depend on one free parameter: the dark matter mass. We study in detail the
case of a singlet scalar as dark matter candidate, which is assumed to be
absolutely stable in flat spacetime due to a discrete $Z_2$ symmetry, but which
may decay in curved spacetimes due to a $Z_2$-breaking non-minimal coupling to
gravity. We calculate the dark matter decay widths and we set conservative
limits on the non-minimal coupling parameter from experiments. The limits are
very stringent and suggest that there must exist an additional mechanism
protecting the singlet scalar from decaying via this gravity portal.
