  We explore here a new mechanism by which the out of equilibrium decay of
heavy gravitinos, followed by possible R-parity violating decays in the Minimal
Supersymmetric Standard Model (MSSM) can generate the baryon asymmetry of the
universe. In this mechanism, gravitino decay produces a CP-asymmetry that is
carried by squarks or sleptons. These particles then decay through R-parity
violating operators generating a lepton asymmetry. The lepton asymmetry is
converted into a baryon asymmetry by weak sphalerons, as in the familiar case
of leptogenesis by Majorana neutrino decays. To ensure that the gravitino
decays while the sphaleron is still in equilibrium, we obtain a lower bound on
the gravitino mass, $m_{3/2} \gtrsim 10^{8} \GeV$, and therefore our mechanism
requires a high scale of SUSY breaking, as well as minimum reheating
temperature after inflation of $T\gtrsim 10^{12} \GeV$ in order to for the
gravitino density to be sufficiently large to generate the baryon asymmetry
today. We consider each of the MSSM's relevant R-parity violating operators in
turn, and derive constraints on parameters in order to give rise to a baryon
asymmetry comparable to that observed today, consistent with low energy
phenomenological bounds on SUSY models.
