COSMOLOGICAL CONSEQUENCES OF SPONTANEOUS LEPTON NUMBER VIOLATION IN SO(10) GRAND UNIFICATION

Cosmological constraints on grand-unified theories with spontaneous le pton number violation are analyzed. We concentrate on SO(10), the simp lest of the models possessing this property. It has been noted previou sly that the consistency of these models with the observed baryon asym metry generically implies strict upper bounds on the light neutrino ma sses. In this paper, we analyze the situation in detail. We find that minimal models of fermion masses face difficulties, but that it is pos sible for these models to generate an adequate baryon asymmetry via no nequilibrium lepton-number-violating processes when the right-handed n eutrino masses are near their maximum possible values. This condition uniquely picks out the minimal gauge symmetry-breaking scheme. A nonmi nimal model is also analyzed, with somewhat different conclusions due to the nature of the imposed symmetries.