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 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.Comment: 22 pages, Latex file, 5 figure
