Quantum Gravity Effects on Fermionic Dark Matter and Gravitational Waves

We explore the phenomenological consequences of breaking discrete global symmetries in quantum gravity (QG). We extend a previous scenario where discrete global symmetries are responsible for scalar dark matter (DM) and domain walls (DWs), to the case of fermionic DM, considered as a feebly interacting massive particle, which achieves the correct DM relic density via the freeze-in mechanism. Due to the mixing between DM and the standard model neutrinos, various indirect DM detection methods can be employed to constrain the QG scale, the scale of freeze-in, and the reheating temperature simultaneously. Since such QG symmetry breaking leads to DW annihilation, this may generate the characteristic gravitational wave background, and hence explain the recent observations of the gravitational wave spectrum by pulsar timing arrays. This work therefore highlights a tantalizing possibility of probing the effective scale of QG from observations.