  We study the evolution of a cosmological baryon asymmetry in leptogenesis
when the right-handed neutrinos are produced in inflaton decays. By performing
a detailed numerical study over a broad range of inflaton-neutrino couplings we
show that the resulting asymmetry can be larger by two orders of magnitude or
more than in thermal leptogenesis, if the reheating temperature T_{RH} is of
the same order as the right-handed neutrino mass M_1. Hence, the lower limit on
the baryogenesis temperature obtained in thermal leptogenesis can be relaxed
accordingly.
