Non-thermal leptogenesis in supersymmetric 3-3-1 model with inflationary scenario

We study a leptogenesis scenario in which the heavy Majorana neutrinos are produced non-thermally in inflaton decays in the supersymmetric economical SU(3)_C X SU(3)_L X U(1)_X model with inflationary scenario, and for this purpose neutrino masses play the key role. Due to the inflaton with mass in the GUT scale, the model under consideration provides successful neutrino masses, which is different from ones without inflationary scenario. The lepton-number-violating interactions among the inflaton and right-handed neutrinos appear at the one-loop level, and this is a reason for non-thermal leptogenesis scenario. The bound followed from the gravitino abundance and the cosmological constraint on neutrino mass/the neutrino oscillation data is m_\nu 3 \simeq \frac{0.05}{\delta_{eff}} eV. By taking the reheating temperature as low as T_R= 10^6 GeV, we get a limit on the ratio of masses of the light heavies neutrino to those of the inflaton to be \fr{M_{R1}}{M_{\phi}} = 0.87.