Cosmological Constraints on the Scale of Supersymmetry Breaking

We consider the cosmological and astrophysical constraints on the decay of massive $E_8 \times E_8^\prime$ superstring axions associated with the hidden sector. We find that decay lifetimes greater than 1 s are ruled out by limits from nucleosynthesis, by limits on the distortion of the cosmic microwave and gamma ray backgrounds and by closure arguments. We conclude that $\Lambda>1.2\times10^{13}\gev$, where $\Lambda$ is the scale of gaugino condensation in the hidden sector. This implies that the scale of supersymmetry breaking is greater than $10^{10}\gev$. Significantly, our result agrees with the value of $5\times 10^{13}\gev$ for $\L$ obtained independently by setting supersymmetric scalar masses equal to $m_W$.