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 $Tgtrsim 10^{12} GeV$ in order to for the gravitino density to be sufficiently large to generate the baryon asymmetry today. We consider each of the MSSMs 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.
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