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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): 

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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 

