SIMBAD references

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, Hubble 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".9x21".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 P_m_ is almost independent of σ₈, for any combination of Ω₀, λ₀, and H₀, indicating that P_m 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.