  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.
