  We investigate a scheme for making leptogenesis by means of the CP violating
decays of the seesaw Majorana neutrinos proposed by Fukugita and Yanagida.
However, in order to avoid the wash-out of the produced lepton number we
propose the production of the Majorana neutrinos to occur non-thermally and
sufficiently late. After this time, in consequence, the B-L (baryon minus
lepton) quantum number becomes a good ``accidental symmetry'' protecting the
asymmetry produced. This non-thermal leptogenesis at late time is realized by a
boson decaying into the Majorana neutrinos with a long lifetime. Suggestively
this boson could correspond to a scalar field which causes the cosmic
inflation, the inflaton, and thus its decay means really the reheating of the
Universe. We find that this mechanism works well even if the lightest Majorana
neutrinos are not produced sufficiently or not present, and the decays of the
heavier seesaw Majorana neutrinos can be responsible to the baryon asymmetry in
the present Universe, as we illustrate by the example of the family replicated
gauge group model.
