  The origin of the hot phase of the early universe remains so far an unsolved
puzzle. A viable option is entropy production through the decays of heavy
Majorana neutrinos whose lifetimes determine the initial temperature. We show
that baryogenesis and the production of dark matter are natural by-products of
this mechanism. As is well known, the cosmological baryon asymmetry can be
accounted for by leptogenesis for characteristic neutrino mass parameters. We
find that thermal gravitino production then automatically yields the observed
amount of dark matter, for the gravitino as the lightest superparticle and
typical gluino masses. As an example, we consider the production of heavy
Majorana neutrinos in the course of tachyonic preheating associated with
spontaneous B-L breaking. A quantitative analysis leads to contraints on the
superparticle masses in terms of neutrino masses: For a light neutrino mass of
10^{-5} eV the gravitino mass can be as small as 200 MeV, whereas a lower
neutrino mass bound of 0.01 eV implies a lower bound of 9 GeV on the gravitino
mass. The measurement of a light neutrino mass of 0.1 eV would rule out heavy
neutrino decays as the origin of entropy, visible and dark matter.
