We discuss baryogenesis via leptogenesis in seesaw models with the heaviest right-chiral neutrino effectively decoupled from the seesaw mechanism and propose a natural bottom-up parametrization, which leads to a simple formula for the CP asymmetry in the decays of the lightest right-chiral neutrino. We show that for successful leptogenesis there is a lower bound on the mass of the lightest right-chiral neutrino. If this neutrino is to be produced thermally after inflation, the bound on its mass can be translated into a lower bound on the reheating temperature of the Universe, which can be in conflict with the upper bound required to avoid the gravitino problem. We also present possible ways of circumventing this difficulty.

PACS numbers: 13.15.+g, 14.60.St, 95.30.Cq, 98.80.-k