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Published online by Cambridge University Press: 19 July 2016
This paper discusses the recent measurement of the number of galaxies vs. redshift and flux and presents new results pertaining to the two dimensionless geometrical quantities that describe the geometry of the conventional big-bang cosmology, the density parameter Ω and the dimensionless form λ = Λ/(3H02) of the cosmological constant. In contrast to the classical redshift-magnitude test as applied to the brightest galaxies in clusters, this new method is able to separate the effects of evolution from geometrical effects and is therefore able to measure the geometry of space. The 95% confidence limits are Ω - λ = 0.9−0 5+0 7 and −1.5 < Ω + λ < 7.1. The principal conclusions are these: (1) For both λ = 0 and inflationary models of the universe, this measurement and primordial nucleosynthesis imply a large density of nonbaryonic matter. (2) Hubble's constant H0 and the age of the universe τ are constrained by 0.60 < H0τ < 0.88 (95% confidence).