Limiting majoron self-interactions from gravitational wave experiments

We show how majoron models may be tested/limited in gravitational wave experiments. In particular,the majoron self-interaction potential may induce a first order phase transition, producing gravitational waves from bubble collisions. We dub such a new scenario the violent majoron model, because it would be associated with a violent phase transition in the early Universe. Sphaleron constraints can be avoided if the global U（1）_（B-L） is broken at scales lower than the electroweak scale, provided that the B-L spontaneously breaking scale is lower than10 TeV in order to satisfy the cosmological mass density bound. The possibility of a sub-electroweak phase transition is practically unconstrained by cosmological bounds and it may be detected within the sensitivity of the next generation of gravitational wave experiments： eLISA, DECIGO and BBO. We also comment on its possible detection in the next generation of electron-positron colliders, where majoron production can be observed from the Higgs portals in missing transverse energy channels.