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Neutrinos are the most elusive particles of the Standard Model. The physics behind their masses remains unknown and requires introducing new particles and interactions. An elegant solution to this problem is provided by the seesaw mechanism. Typically considered at a high scale, it is potentially testable in gravitational wave experiments by searching for a spectrum from cosmic strings, which offers a rather generic signature across many high-scale seesaw models. Here we consider the possibility of a low-scale seesaw mechanism at the PeV scale, generating neutrino masses within the framework of a model with gauged U(1) lepton number. In this case, the gravitational wave signal at high frequencies arises from a first order phase transition in the early Universe, whereas at low frequencies it is generated by domain wall annihilation, leading to a double-peaked structure in the gravitational wave spectrum. The signals discussed here can be searched for in upcoming experiments, including gravitational wave interferometers, pulsar timing arrays, and astrometry observations. 

The nature of dark matter remains one of the greatest unsolved mysteries in elementary particle physics. It might well be that the dark matter particle belongs to a dark sector completely secluded or extremely weakly coupled to the visible sector. We demonstrate that gravitational waves arising from first-order phase transitions in the early Universe can be used to look for signatures of dark sector models connected to neutron physics. This introduces a new connection between gravitational-wave physics and nuclear physics experiments. Focusing on two particular extensions of the Standard Model with dark U(1) and SU(2) gauge groups constructed to address the neutron lifetime puzzle, we show how those signatures can be searched for in future gravitational-wave and astrometry experiments.