Testing unification and dark matter with gravitational waves

We propose to search for a new type of gravitational wave signature relevant for particle physics models with symmetries broken at vastly different energy scales. The spectrum contains a characteristic doublepeak structure consisting of a sharp peak from domain walls and a smooth bump from a first order phase transition in the early universe. We demonstrate how such a gravitational wave signal arises in a new theory unifying baryon number and color into an SU(4) gauge group broken at the multi-TeV scale, and with the lepton number promoted to an SU(2) gauge symmetry broken at the multi-EeV scale. The model contains two types of dark matter particles, explains the observed domination of matter over antimatter in the Universe, and accommodates nonzero neutrino masses. We discuss how future gravitational wave can be utilized to look for this novel signature.