Implications of the Red-Shift-Number Test for Cosmology

This Letter discusses the recent measurement of the number of galaxies versus red shift and flux for cosmological models with a nonzero cosmological constant $\Lambda$ and pressureless matter. The main conclusions are these: (1) If space is flat as the inflationary model predicts, then the density parameter $\Omega ={0.9}_{-0.2\mathrm{}}^{+0.4\mathrm{}}$ and $\frac{\Lambda }{\left(3\mathrm{}{H}_0^2\right)}={0.1}_{-0.4\mathrm{}}^{+0.2\mathrm{}}$. (95%-confidence intervals are used throughout.) (2) For both inflationary and $\Lambda =0\mathrm{}$ models, the present result and primordial nucleosynthesis are consistent only if a large density of nonbaryonic matter exists. (3) Without any assumptions about $\Lambda$, the age of the Universe $t$ and Hubble's constant $H_0$ are constrained by $0.60<t{H}_0<0.88\mathrm{}$.