# Neutrino mass and Gravitational waves from first order phase transitions

We show how Majoron models may be tested/limited in gravitational waves experiments. In particular, the Majoron self-interaction potential may induce a first order phase transition, producing gravitational waves from bubble collisions. We dubbed such a new scenario {\it violent Majoron model}, because it would be associated to 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 than $10\, {\rm TeV}$ 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 next generation of gravitational waves experiments: eLISA, DECIGO and BBO. We also comment on the possible detection in CEPC collider, where Majorons's production can be observed from Higgs' portals in missing transverse energy channels.