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 $M_{\rm DM}\lesssim$ 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'.
