Planck Scale Effects on the Majoron
  The hypothesis that non-perturbative gravitational effects lead to explicit breaking of global symmetries is considered in the context of Majoron models. We find that the nonvanishing Majoron mass generated by these effects can overclose the universe unless the massive Majoron is unstable. The cosmological mass density constraints can then be satisfied only if $V_{BL} < 10$ TeV, where $V_{BL}$ is the scale of $B-L$ symmetry breaking. 
E.Kh. Akhmedov, Z.G. Berezhiani, R.N. Mohapatra and G. Senjanovic