  We show that spontaneous breaking of global $B-L$ symmetry responsible for
small neutrino masses via the seesaw mechanism provides a unified picture of
hybrid inflation and dark matter if the scale of $B-L$ breaking is close to the
GUT scale. The majoron which acquires a small mass in the milli-eV range due to
Planck scale breaking of $B-L$ is the dark matter candidate. The coupling of
the majoron field to the neutrino induces a small violation of CPT and Lorentz
invariance at the present epoch. We discuss some of the phenomenological and
cosmological implications of the model.
