Inflaton mass in the νMSM inflation

We analyze the reheating in the modification of the νMSM (Standard Model with three right handed neutrinos with masses below the electroweak scale) where one of the sterile neutrinos, which provides the Dark Matter, is generated in decays of the additional inflaton field. We deduce that due to rather inefficient transfer of energy from the inflaton to the Standard Model sector reheating tends to occur at very low temperature, thus providing strict bounds on the coupling between the inflaton and the Higgs particles. This in turn translates to the bound on the inflaton mass, which appears to be very light 0.1GeV≲mI≲10GeV, or slightly heavier then two Higgs masses 300GeV≲mI≲1000GeV.