Testing unification and dark matter with gravitational waves

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