Leptophilic dark matter from gauged lepton number: Phenomenology and gravitational wave signatures

New gauge symmetries often appear in theories beyond the Standard Model. Here we study a model where lepton number is promoted to a gauge symmetry. Anomaly cancellation requires the introduction of additional leptons, the lightest of which is a natural leptophilic dark matter candidate. We perform a comprehensive study of both collider and dark matter phenomenology. Furthermore we find that the model exhibits a first order lepton number breaking phase transition in large regions of parameter space. The corresponding gravitational wave signal is computed, and its detectability at LISA and other future GW detectors assessed. Finally we comment on the complementarity of dark matter, collider and gravitational wave observables, and on the potential reach of future colliders.