  This paper investigates non-thermal leptogenesis from inflaton decays in the
minimal extension of the canonical type-I seesaw model, where a complex singlet
scalar $\phi$ is introduced to generate the Majorana masses of right-handed
neutrinos (RHNs) and to play the role of inflaton. First, we systematically
study non-thermal leptogenesis with the least model dependence. We give a
general classification of the parameter space and find four characteristic
limits by carefully examining the interplay between inflaton decay into RHNs
and the decay of RHNs into the standard-model particles. Three of the four
limits are truly non-thermal, with a final efficiency larger than that of
thermal leptogenesis. Two analytic estimates for these three limits are
provided with working conditions to examine the validity. In particular, we
find that the {\it strongly non-thermal RHNs} scenario occupies a large
parameter space, including the oscillation-preferred $K$ range, and works well
for a relatively-low reheating temperature $T^{}_{\rm RH} \geq 10^3~{\rm GeV}$,
extending the lower bound on the RHN mass to $2\times 10^{7}~{\rm GeV}$. The
lepton flavor effects are discussed. Second, we demonstrate that such a unified
picture for inflation, neutrino masses, and baryon number asymmetry can be
realized by either a Coleman-Weinberg potential (for the real part of $\phi$)
or a natural inflation potential (for the imaginary part of $\phi$). The
allowed parameter ranges for successful inflation and non-thermal leptogenesis
are much more constrained than those without inflationary observations. We find
that non-thermal leptogenesis from inflaton decay offers a testable framework
for the early Universe. It can be further tested with upcoming cosmological and
neutrino data. The model-independent investigation of non-thermal leptogenesis
should be useful in exploring this direction.
