Γ$_{3}$$_{/}$$_{2}$ ≃ m 3 / $_{2}$/ 4 M 2 $_{P}$, see [311]. If m$_{3}$$_{/}$$_{2}$ < 50 TeV, the gravitinos decay during or after BBN [26, 810], which can ruin its successful predictions for the primordial abundance of light elements. If the gravitinos decay radiatively, the most stringent bound, ( n$_{3}$$_{/}$$_{2}$/s ) ≤ 10 − 14 − 10 − $^{12}$, arises for m$_{3}$$_{/}$$_{2}$ ≃ 100 GeV − 1 TeV [320]. On the other hand, much stronger bounds are derived if the gravitinos mainly decay through the hadronic modes. In particular, for a hadronic branching ratio ≃ 1, and in the same mass range, ( n$_{3}$$_{/}$$_{2}$/s ) ≤ 10 − 16 − 10 − 15 will be required [313, 314]. 

For a radiatively decaying gravitino the tightest bound ( n$_{3}$$_{/}$$_{2}$/s ) ≤ 10 − 14 arises when m$_{3}$$_{/}$$_{2}$ ≃ 100 GeV [320]. Following Eq. (412) the bound on reheat temperature becomes: T$_{R}$ ≤ 10 10 GeV. For a TeV gravitino which mainly decays into gluon-gluino pairs (allowed when m$_{3}$$_{/}$$_{2}$ > M$_{˜}$ $_{g}$) a much tighter bound ( n$_{3}$$_{/}$$_{2}$/s ) ≤ 10 − 16 is obtained [313, 314], which requires quite a low reheat temperature: T$_{R}$ ≤ 10 6 GeV. 

The gravitino will be stable if it is the LSP, where R -parity is conserved. The gravitino abundance will in this case be constrained by the dark matter limit, Ω$_{3}$$_{/}$$_{2}$ h 2 ≤ 0 . 12, leading to 

For m$_{3}$$_{/}$$_{2}$ < M$_{˜}$ $_{g}$, the helicity ± 1 / 2 states dominate the total gravitino abundance. As an example, consider the case with a light gravitino, m$_{3}$$_{/}$$_{2}$ = 100 KeV, which can arise very naturally in gauge-mediated models [719]. If M$_{˜}$ g ≃ 500 GeV, see Eq. (412), a very severe constraint, T$_{R}$ ≤ 10 4 GeV, will be obtained on the reheat temperature $^{90 91}$. 

