If one assumes a spontaneously broken local supersymmetry, big-bang cosmology implies that the universe is filled with a gravitino ($g_{\frac{3}{2}}$) gas—possibly its dominant constituent. From the observational bound on the cosmological mass density it follows that $m_{g_{\frac{3}{2}}}\lesssim 1$ keV. Correspondingly, the supersymmetry breaking parameter $F$ satisfies $\sqrt{F}\lesssim 2\times {10}^3$ TeV, requiring new supersymmetric physics in the teraelectronvolt energy region. An exact sum rule is derived and used to estimate the threshold and cross section for the production of the new states.

• Received 17 August 1981

DOI:https://doi.org/10.1103/PhysRevLett.48.223