Neutrino mass, dark matter and inflation
  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. 
D. Kazanas, R. N. Mohapatra, S. Nasri and V. L. Teplitz