  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.
