The Implications of Direct Red-Shift Measurement of γ-ray Bursts

The recent discoveries of X-ray and optical counterparts for GRBs, and a possible discovery of a host galaxy, implies that a direct measurement of the red-shift of some GRBs host galaxies is eminent. We discuss the implications of such measurements. They could enable us to determine the GRBs luminosity distribution, the variation of the rate of GRBs with cosmic time, and even, under favorable circumstances, to estimate $\Omega$. Using GRB970508 alone, and assuming standard candles, we constrain the intrinsic GRB evolution to $\rho(z)=(1+z)^{-0.5\pm0.7}$.