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 $^{90 91}$. 90 Gravitinos could also be produced by non-perturbative processes, as was first described in [789] for helicity ± 3 / 2 component of gravitino. Later the production of the helicity ± 1 / 2 state were also studied [658, 790– 794, 811]. The helicity ± 1 / 2 component obtains a major contribution from the inflatino (superpartner of inflaton), however the inflatino decays with the same rate as that of the inflaton, therefore the ± 1 / 2 abundance does not any major role [792–794, 811]. A very late decay of inflatino could however be possible, as argued in [792–794]. In [812], it was argued that if the inflatino and gravitino were not LSP, then late off-shell inflatino and gravitino mediated decays of heavy relics could be significant. 91 Recently, non-thermal abundance of gravitino from a modulus decay has been revisited [813–816]. The gravitino abundance is given by: Y$_{3}$$_{/}$$_{2}$ ∼ B$_{3}$$_{/}$$_{2}$ 3 T R 4 $_{m$_{φ}$}$, where B$_{3}$$_{/}$$_{2}$ is the branching ratio into gravitino and would be B$_{3}$$_{/}$$_{2}$ = 10 − $^{2}$− 1 with the mixing between modulus and the SUSY-breaking field, where we have used an approximation n$_{φ}$/s ∼ (3 T$_{R}$/ 4 m$_{φ}$ ), essentially the moduli decay is creating all the entropy of the universe. The branching ratio of the gravitino production from a modulus decay is little more contentious than one would naively expect. For B$_{3}$$_{/}$$_{2}$ ∼ 1, there is a possibility of overproducing gravitinos. However, as it was pointed out in Ref. [815], the decay rate generically obtains a helicity suppression. The precise value depends on the details of the SUSY breaking hidden sector. There are well known examples of 193