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Evidence for a stochastic gravitational wave background in the nHz frequencyband is recently reported by four pulsar timing array collaborations NANOGrav,EPTA, CPTA, and PPTA. It can be interpreted by gravitational waves fromcollapsing domain walls in the early universe. We assume such domain wallsarising from the spontaneous breaking of a $Z_2$ symmetry in a scalar fieldtheory, where a tiny $Z_2$-violating potential is required to make domain wallsunstable. We propose that this $Z_2$-violating potential is radiatively inducedby a feeble Yukawa coupling between the scalar field and a fermion field, whichis also responsible for dark matter production via the freeze-in mechanism.Combining the pulsar timing array data and the observed dark matter relicdensity, we find that the model parameters can be narrowed down to smallranges.

Nano-Hertz gravitational waves from collapsing domain walls associated with freeze-in dark matter in light of pulsar timing array observations