Astrophysical Limits on Gravitino Mass

We calculate exotic cooling rates of stars due to photo-production of light particles (mostly scalars and pseudoscalars) which originate from the hidden sector of no scale supergravity theories. Using this we can restrict the gravitino mass $m_{3/2}$. The range of eliminated values of $m_{3/2}$ stretches over six orders of magnitude and is given by $\displaystyle{2 \times 10^8 < {m_{\tilde g} \over m_{3/2}} < 6 \times 10^{13}}$, $m_{\tilde g}$ being the gluino mass. Combining our result with the earlier analysis from colliders ($\displaystyle{ {m_{\tilde g} \over m_{3/2}} < 2.7 \times 10^{14}}$) we conclude that $\displaystyle{{m_{\tilde g} \over m_{3/2}} < {\cal O}(10^8)}$ except for a narrow window around $10^{14}$. Together with the current experimental limit on $m_{\tilde{g}}$ and cosmological constraints on $m_{3/2}$, albeit model dependent, our analysis shows that a light gravitino is on the verge of being ruled out.