Non-thermal production of lepton asymmetry and dark matter in minimal seesaw with right handed neutrino induced Higgs potential

Within Type-I seesaw mechanism, Higgs mass can be dynamically generated via quantum effects of the right handed neutrinos assuming the potential is nearly conformal at the Ultra-Violet. The scenario, named as the "Neutrino Option" allows RH neutrino mass scale upto $M\lesssim$ ${10}^7$ GeV to be consistent with light neutrino masses, mixing and Higgs mass. Therefore, it is not consistent with standard hierarchical thermal leptogenesis. Parameter space for thermal resonant leptogenesis is highly constrained in this model. We point out that non-thermal pair production of RH neutrinos from inflaton decay corresponds in general to a mild degree of resonance in the CP asymmetry parameter and allows RH mass scale to be smaller more than by an order of magnitude than the thermal strong resonance case. Within the similar parameter space of thermal leptogenesis, RH neutrinos can also be produced from inflaton decay along with a Dark Matter having mass $M_{DM}\lesssim$320 MeV. The main constraint in the latter scenario comes from the Ly$\alpha$ constraints on Dark Matter free streaming. We show in addition, that the Neutrino Option introduces a 'phantom window' for the RH mass scale, in which contrary to the usual scenarios, CP asymmetry parameter for leptogenesis decreases with the increase of the RH mass scale and minimally fine-tuned seesaw models naturally exhibit this 'phantom window'.