R-parity violation and the cosmological gravitino problem

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.