Résumé
The Standard Model of particle physics was developped in the 1970s'. Despite many experimental successes, it presents many problems that can only be solved with models beyond the Standard Model. Supersymmetry is an interesting candidate, postulating a new symmetry between fermions and bosons. This model can also have interesting applications in cosmology. It offers potentially good candidates for dark matter, what represents 25\% of the energy density of the Universe, and its nature is unknown. Another cosmological problem is the lithium problems in Big Bang Nucleosynthesis describing the production of light elements in the first seconds of the Universe. The lithium abundance predicted by the theory is inconsistent with observations. I study a scenario in which a supersymmetric particle, the gravitino, is the candidate for dark matter and the production of this particle through the decay of other supersymmetric particles may solve the lithium problems.