Neutrino masses, leptogenesis and dark matter from small lepton number violation?

We consider the possibility of simultaneously addressing the baryon asymmetry of the Universe, the dark matter problem and the neutrino mass generation in minimal extensions of the Standard Model via sterile fermions with (small) total lepton number violation. Within the framework of Inverse and Linear Seesaw models, the small lepton number violating parameters set the mass scale of the active neutrinos, the efficiency of leptogenesis through a small mass splitting between pairs of sterile fermions as well as the mass scale of a sterile neutrino dark matter candidate. We provide an improved parametrization of these seesaw models taking into account existing experimental constraints and derive a linearized system of Boltzmann equations to describe the leptogenesis process, which allows for an efficient investigation of the parameter space. This in particular enables us to perform a systematic study of the strong washout regime of leptogenesis. Our study reveals that one can have a successful leptogenesis at the temperature of the electroweak scale through oscillations between two sterile states with a natural origin of the (necessary) strong degeneracy in their mass spectrum. The minimal model however requires a non-standard cosmological history to account for the relic dark matter. Finally, we discuss the prospect for neutrinoless double beta decay and for testing, in future experiments, the values of mass and different active-sterile mixings required for successful leptogenesis.