  Based on the R-parity violation option of the minimal supersymmetric Standard
Model, we examine the scenario where the massive gravitino, relic from the hot
big-bang, is the lightest supersymmetric particle and can decay through one or
several of the trilinear R-parity violating interactions. We calculate the
rates of the gravitino decay via the various three-body decay channels with
final states involving three quarks and/or leptons. By taking into account the
present constraints on the trilinear R-parity violating coupling constants and
assuming the gravitino and scalar superpartner masses do not exceed ${\cal
O}(10TeV)$, it turns out that the gravitinos could easily have decayed before
the present epoch but not earlier than the big-bang nucleosynthesis one.
Therefore, the considered scenario would upset the standard big-bang
nucleosynthesis and we conclude that it does not seem to constitute a natural
solution for the cosmological gravitino problem.
