Evolution of the Luminosity Density in the Universe: Implications for the Nonzero Cosmological Constant

We show that evolution of the luminosity density of galaxies in the universe provides a powerful test for the geometry of the universe. Using reasonable galaxy evolution models of population synthesis which reproduce the colors of local galaxies of various morphological types, we have calculated the luminosity density of galaxies as a function of redshift $z$. Comparison of the result with recent measurements by the Canada-France Redshift Survey in three wavebands of 2800{\AA}, 4400{\AA}, and 1 micron at z<1 indicates that the \Lambda-dominated flat universe with \lambda_0 \sim 0.8 is favored, and the lower limit on \lambda_0 yields 0.37 (99% C.L.) or 0.53 (95% C.L.) if \Omega_0+\lambda_0=1. The Einstein-de Sitter universe with (\Omega_0, \lambda_0)=(1, 0) and the low-density open universe with (0.2, 0) are however ruled out with 99.86% C.L. and 98.6% C.L., respectively. The confidence levels quoted apply unless the standard assumptions on galaxy evolution are drastically violated. We have also calculated a global star formation rate in the universe to be compared with the observed rate beyond z \sim 2. We find from this comparison that spiral galaxies are formed from material accretion over an extended period of a few Gyrs, while elliptical galaxies are formed from initial star burst at z >~ 5 supplying enough amount of metals and ionizing photons in the intergalactic medium.