Key points are not available for this paper at this time.
Inflationary cosmological theories predict and some more general aesthetic criteria suggest that the large-scale spatial curvature of the universe k should be accurately zero (i. e. , flat), a condition which is satisfied when the universe's present mean density ρᵇar^₀_ and the value of the cosmological constant LAMBDA have certain pairs of values. Available data on the frequency of multiple image lensing of high-redshift quasars by galaxies suggest that the cosmological constant cannot make a dominant contribution to producing a flat universe. In particular, if the mean density of the universe is as small as the baryon density inferred from standard cosmic nucleosynthesis calculations or as determined from typical dynamical studies of galaxies and galaxy clusters, then a value of LAMBDA large enough to produce a k = 0 universe would result in a substantially higher frequency of multiple-image lensing of quasars than has been observed so far. Shortcomings of the available lens data and uncertainties concerning galaxy properties allow some possibility of escaping this conclusion, but systematic searches for gravitational lenses and continuing investigations of galaxy mass distributions should soon provide decisive information. It is also noted that nonzero curvature cosmological models can account for the observed frequency of galaxy-quasar lens systems and for a variety of other constraints.
Edwin L. Turner (Sat,) studied this question.