The cosmological realization of the spontaneous breaking of B-L, the
difference of baryon and lepton number, can successfully generate the
initial conditions of the hot early universe. If B-L is broken at the
grand unification scale, the false vacuum phase yields hybrid inflation,
ending in tachyonic preheating. The dynamics of the B-L breaking Higgs
field and thermal processes produce an abundance of heavy neutrinos
whose decays generate entropy, baryon asymmetry and gravitinos.
Depending on the underlying SUSY spectrum, either the gravitinos
themselves or WIMPs from gravitino decays can yield the observed DM
abundance. In this talk, I discuss the B-L phase transition for the full
supersymmetric Abelian Higgs model, focusing on its cosmological
consequences. In particular, I present a time-resolved description of
all particle abundances, and show that the consistency of hybrid
inflation, leptogenesis and dark matter implies relations between
neutrino parameters and superparticle masses.