  In this essay we show that quantum gravity and the spin-statistics theorem
have very interesting consequences for dark matter candidates. Quantum gravity
can lead to fifth force type interactions that lead to a lower bound on the
masses of bosonic candidates. In the case of fermions, the spin-statistics
theorem leads to a lower bound on fermion masses. For both bosonic and
fermionic dark matter candidates, quantum gravity leads to a decay of dark
matter particles. A comparison of their lifetime with the age of the universe
leads to an upper bound on their masses. For singlet scalar dark matter fields,
we find $10^{-3}{\rm eV} \lesssim m\lesssim 10^{7}{\rm eV}$.
