New Astrophysical Constraints on the Mass of the Superlight Gravitino
  In some supergravity models, the superlight gravitino is accompanied by a light weakly coupled scalar (S) and pseudo-scalar (P) particle. The coupling of these particles to matter is inversely proportional to the product of the gravitino mass and the Planck mass. As a result, their emission from the stars and supernovae via the photon electron scattering reaction for certain ranges of the gravitino mass can become the dominant energy loss mechanism in contradiction with observations thereby ruling out those mass values for the gravitino. For scalar and/or pseudo-scalar masses between 10 MeV and a keV, the SN1987A observations exclude the gravitino mass range from 0.03 eV to 30 eV whereas if the S/P masses are less than a keV, constraints of stellar energy loss can exclude the gravitino masses ranging from $3\times 10^{-6}$ eV to 50 eV for the photino mass of 100 GeV. We also find that for S/P mass less than an MeV, Big Bang Nucleosynthesis constraints imply a gravitino mass larger than one eV. These are the most stringent bounds to date on the gravitino mass in this class of models. 
J. A. Grifols, R. N. Mohapatra and A. Riotto