abundance of χ , normalized by the entropy density, s , is given by [122] where we have used Eq. (437). For flat direction(s) VEV ≥ 10 12 GeV, slow thermalization results in a low reheat tem- perature, i.e T$_{R}$ ≤ 10 9 GeV, which is compatible with the BBN bounds on thermal gravitino production. However gravitinos are also produced during the quasi-thermal phase prior to a complete thermalization of the reheat plasma. Generically gravitinos are produced from the scatterings of gauge, gaugino, fermion and sfermion quanta with a cross-section ∝ 1 /M 2 $_{P}$. During the quasi-thermal phase, the gauge and gaugino quanta have large masses ∼ α 1 / $^{2}$ϕ$_{d}$ (induced by the flat direction VEV) at a time most relevant for the gravitino production, i.e., when H ≃ Γ$_{d}$, therefore, they decay to lighter fermions and sfermions at a rate ∼ α 3 / $^{2}$ϕ2$_{d}$/m$_{φ}$ , where α 3 / $^{2}$ϕ$_{d}$ is the decay width at the rest frame of gauge/gaugino quanta, and ϕ$_{d}$/m$_{φ}$ is the time-dilation factor. The decay rate is ≫ Γ$_{d}$, thus gauge and gaugino quanta decay almost instantly upon production, and they will not participate in the gravitino production. As a consequence, production of the helicity ± 1 / 2 states will not be enhanced in a quasi-thermal phase as scatterings with a gauge-gaugino-gravitino vertex will be absent $^{102}$. The following channels contribute to the gravitino production [309]: (a) fermion + anti- sfermion → gravitino + gauge field , (b) sfermion + anti-fermion → gravitino + gauge field , (c) fermion + anti-fermion → gravitino + gaugino , (d) sfermion + anti-sfermion → gravitino + gaugino . The total cross-section involves cross-sections for multiplets comprising the LH (s)quarks Q , RH up-type (s)quarks u , RH down-type (s)quarks d , LH (s)leptons L , RH (s)leptons e and the two Higgs/Higgsino doublets H$_{u}$, H$_{d}$ . Since particles and anti-particles associated to the bosonic and fermionic components of the multiplets which belong to an irreducible 2. Gravitino production 102 Otherwise gauge and/or gaugino quanta in the initial state (particularly scattering of two gluons) have the largest production cross-section [309–312]. 205 n$_{χ}$ s ∼ $_{10}$− 5 ( 228 . 75 A ) 5 / $^{4}$∑ i,j [∫ T max T min A i A j 〈 v$_{rel}$ $^{σ$_{ij}$}$→ χ 〉 M$_{P}$ dT ] , (439)