 100  1000  10000  100000  1e+06  1e+07  1e+08  20  40  60  80  100  120  140 j = Mt/ Higgs: Bosons: B Fermions: F FIG. 21: Evolution of the energy density transferred into the gauge bosons and into the fermions as a function of j , for λ = 0 . 2 and ξ $_{= 44700}$√$_{λ}$$_{. All densities are in units of}$ M 4 [124]. as a test bed where some of the SUSY particles can be tested from the success of BBN, a well known example is the gravitino problem in the context of a SUSY cosmology. 1. Gravitino problem The gravitino is a spin-3 / 2 partner of a graviton, which is coupled to the SM particles with the gravitational strength. Gravitinos with both the helicities can be produced from a thermal bath. There are many scattering channels which include fermion, sfermion, gauge and gaugino quanta all of which have a cross-section ∝ 1 /M 2 P [309–311], and [312], which results in a gravitino abundance (up to a logarithmic correction): Helicity ± 3 2 : n$_{3}$$_{/}$$_{2}$ s ≃ ( T$_{R}$ 10 10 GeV ) $_{10}$− $^{12}$, (full equilibrium) Helicity ± 1 2 : n$_{3}$$_{/}$$_{2}$ s ≃ 1 + M 2 ˜ g 12 m 2 3 / 2 )( T$_{R}$ 10 10 GeV ) $_{10}$− $^{12}$; (412) where M$_{˜}$ g is the gluino mass. Note that for M$_{˜}$ g ≤ m$_{3}$$_{/}$$_{2}$ both the helicity states have essentially the same abundance, while for M$_{˜}$ g ≫ m$_{3}$$_{/}$$_{2}$ production of helicity ± 1 / 2 states is enhanced due to their Goldstino nature $^{89}$. An unstable gravitino decays to particle-sparticle pairs, and its decay rate is given by 89 Since the cross-section for the gravitino production is ∝ $_{M}$− 2 P , the production rate at a temperature, T , and the abundance of the gravitinos produced within one Hubble time will be ∝ T 3 and ∝ T respec- tively. This implies that the gravitino production is efficient at the highest temperature of the radiation- dominated phase of the universe, i.e. T$_{R}$ . 192