If the gravitino is sufficiently light and stable it will behave as an effective massless neutrino species at the time of nucleosynthesis. Depending on the temperature at which it decouples from the thermal bath in the early universe, the gravitino mass will be bounded by the primordial 4He abundance. Assuming a conservative estimate that the number of neutrino families, Nv < 3.6, superlight gravitinos with a mass m3/2 ≲ 10-6 eV are ruled out. This bound is weaker than previous estimates because the Goldstino annihilation cross section was overestimated.
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We would like to thank Ganesh Devaraj, Marty Einhorn and Steve Martin for useful conversations. This work was supported by the U.S. Department of Energy at the University of Michigan.