Goldstino Decoupling in Spontaneously Broken Supergravity Theories

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 $^4$He abundance. Assuming a conservative estimate that the number of neutrino families, $N_\nu < 3.6$, superlight gravitinos with a mass $m_{3/2} \lesssim 10^{-6}$eV are ruled out. This bound is weaker than previous estimates because the Goldstino annihilation cross section was overestimated.