Towards a systematic study of non-thermal leptogenesis from inflaton decays

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.