ar X iv : h ep - p h / 01 07 28 6 v 1 2 7 Ju l 2 00 1 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 supersym-metric 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 O(10T eV), 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.