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We propose a novel scenario of Dark Matter production naturally connectedwith generation of gravitational waves. Dark Matter is modelled as a realscalar, which interacts with the hot primordial plasma through a portalcoupling to another scalar field. For a particular sign of the coupling, thissystem exhibits an inverse second order phase transition. The latter leads toan abundant Dark Matter production, even if the portal interaction is so weakthat the freeze-in mechanism is inefficient. The model predicts domain wallformation in the Universe, long time before the inverse phase transition. Thesedomain walls have a tension decreasing with time, and completely disappear atthe inverse phase transition, so that the problem of overclosing the Universeis avoided. The domain wall network emits gravitational waves withcharacteristics defined by those of Dark Matter. In particular, the peakfrequency of gravitational waves is determined by the portal coupling constant,and falls in the observable range for currently planned gravitational wavedetectors.

Beyond freeze-in: Dark Matter via inverse phase transition and gravitational wave signal