Could neutrinos be related to inflation, dark matter (DM), and the baryon asymmetry of the universe? I present a minimal model where all these connections are made, with GeV-scale heavy neutral leptons (HNLs) as the mediator. The model predicts that one HNL is a stable DM candidate, if the lightest neutrino is massless, and the DM density may be related to the cosmic neutrino asymmetry. The mixing of neutrinos and HNLs can be probed in future intensity experiments like SHiP. The model can also explain anomalous events seen in the KOTO experiment's search for $K_L\to\pi^0\nu\bar\nu$.