Résumé
We show that novel paths to dark matter generation and baryogenesis are open when the Standard Model is extended with three sterile neutrinos $N_i$ and a charged scalar $\delta^+$. Specifically, we propose a new production mechanism for the dark matter particle --a multi-keV sterile neutrino, $N_1$-- that does not depend on the active-sterile mixing angle and does not rely on a large primordial lepton asymmetry. Instead, $N_1$ is produced, via freeze-in, by the decays of $\delta^+$ while it is in equilibrium in the early Universe. In addition, we demonstrate that, thanks to the couplings between the heavier sterile neutrinos $N_{2,3}$ and $\delta^+$, baryogenesis via leptogenesis can be realized close to the electroweak scale. The lepton asymmetry is generated either by $N_{2,3}$-decays for masses $M_{2,3}\gtrsim$ TeV, or by $N_{2,3}$-oscillations for $M_{2,3}\sim$ GeV. Experimental signatures of this scenario include an X-ray line from dark matter decays, and the direct production of $\delta^+$ at the LHC. This model thus describes a minimal, testable scenario for neutrino masses, the baryon asymmetry, and dark matter.