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Implications of Quantum Gravity for Dark Matter

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 $10^{-3}{\rm eV} \lesssim m\lesssim 10^{7}{\rm eV}$.