  Recently a new model of "Affleck-Dine inflation" was presented, that produces
the baryon asymmetry from a complex inflaton carrying baryon number, while
being consistent with constraints from the cosmic microwave background. We
adapt this model such that the inflaton carries lepton number, and communicates
the lepton asymmetry to the standard model baryons via quasi-Dirac heavy
neutral leptons (HNLs) and sphalerons. One of these HNLs, with mass $\lesssim
4.5\,$GeV, can be (partially) asymmetric dark matter (DM), whose asymmetry is
determined by that of the baryons. Its stability is directly related to the
vanishing of the lightest neutrino mass. Neutrino masses are generated by
integrating out heavy sterile neutrinos whose mass is above the inflation
scale. The model provides an economical origin for all of the major ingredients
missing from the standard model: inflation, baryogenesis, neutrino masses, and
dark matter. The HNLs can be probed in fixed-target experiments like SHiP,
possibly manifesting $N$-$\bar N$ oscillations. A light singlet scalar, needed
for depleting the DM symmetric component, can be discovered in beam dump
experiments and searches for rare decays, possibly explaining anomalous events
recently observed by the KOTO collaboration. The DM HNL is strongly constrained
by direct searches, and could have a cosmologically interesting
self-interaction cross section.
