  In this study, we investigate a scenario that dark matter (DM) has only
gravitational interaction. In the framework of effective field theory of
gravity, we find that DM is still stable at tree level even if there is no
symmetry to protect its longevity, but could decay into standard model
particles due to gravitational loop corrections. The radiative corrections can
lead to both higher- and lower-dimensional effective operators. We also first
explore how DM can be produced in the early universe. Through gravitational
interaction at high temperature, DM is then found to have mass around TeV
$\lesssim m_X \lesssim 10^{11}$GeV to get the right relic abundance. When DM
decays, it mostly decays into gravitons, which could be tested by current and
future CMB experiments. We also estimate the resulting fluxes for cosmic rays,
gamma-ray and neutrino.
