Using a multiple lens-plane algorithm, we study light propagation in inhomogeneous universes, for 43 different COBE-normalized cold dark matter models, with various values of the density parameter Ω0, cosmological constant λ0, Rubble constant H0, and rms density fluctuation σ8. This is the largest cosmological parameter survey ever undertaken in this field. We performed a total of 3798 experiments, each experiment consisting of propagating a square beam of angular size 21″.9 × 21″.9 composed of 116,281 light rays from the observer up to redshift z = 3. These experiments provide statistics of the magnification, shear, and multiple imaging of distant sources. The results of these experiments can be compared with observations and eventually help to constrain the possible values of the cosmological parameters. In addition, they provide insight into the gravitational lensing process and its complex relationship with the various cosmological parameters. Our main results are the following: (1) The magnification distribution depends mostly upon λ0 and σ8. As σ8 increases, the low tail of the magnification distribution shifts toward lower magnifications, while the high tail is hardly affected. The magnification distribution also becomes wider as λ0 increases. This effect is particularly large for models with λ0 = 0.8. (2) The magnification probability Pm is almost independent of σ8, for any combination of Ω0, λ0, and H0, indicating that Pm does not depend strongly upon the amount of large-scale structure. (3) The shear distribution, like the magnification distribution, depends mostly upon λ0 and σ8. The shear distribution becomes wider with increasing σ8 and increasing λ0. The similarities between the properties of the magnification and shear distributions suggest that both phenomena are caused by weak lensing. (4) About 0.3% of sources have multiple images. The double-image probability P2 increases strongly with λ0 and is independent of Ω0, H0, and σ8. (5) The distribution of image separations depends strongly upon λ0 and is independent of σ8. Summarizing these results, we find that (a) The properties of gravitational lensing, both weak and strong, depend much more strongly upon λ0 than any other cosmological parameter, and (b) magnification and shear are examples of weak lensing caused primarily by the distribution of background matter, with negligible contribution from galaxies, while multiple images and rings are examples of strong lensing, caused by direct interaction with galaxies, with negligible contribution from the background matter. Observations of weak lensing can be used to determine the cosmological constant and the density structure of the universe, while observations of strong lensing can be used to determine the cosmological constant and the internal structure of galaxies and clusters. Gravitational lensing depends much more weakly upon Ω0 and H0 than σ8 and λ0, making a determination of these parameters from observations more difficult.
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