Annu. Rev. Astron. Astrophys. 1999. 37: 127-189
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4. LARGE-SCALE STRUCTURES AND COSMIC SHEAR

The idea that mass condensations and the geometry of the Universe can alter light bundles and distort the images of distant galaxies was emphasized by Kristian & Sachs (1966), and later by Gunn (1967), Blandford & Jaroszynski (1981), who first gave a quantitative estimate of the amplitude of this effect. Kristian (1967) looked at this effect on photographic plates of six clusters of galaxies using the Palomar Telescope, but found nothing significant. Valdes et al (1983) were the first to attempt to measure a coherent alignment of distant galaxies generated by large-scale structures. They used about 40,000 randomly selected field galaxies with J magnitudes between 22.5 and 23.5, but, like Kristian, they did not find any conclusive signal. These negative measurements were not definitely interpreted as important cosmological constraints on the curvature and the mass distribution in our Universe, but instead as a result of technical limitations related to the poor image quality of the photographic data. Indeed, the recent weak lensing analysis produced by a supercluster candidate done by Kaiser et al (1998) seems to show that large-scale structures produce gravitational shear which is already detectable. Numerical simulations by Schneider & Weiss (1988) using point-mass models, or by Babul & Lee (1991) using a smooth mass distribution, showed that both the ellipticity distribution and the apparent luminosity function of distant galaxies could be modified, in particular if the fraction of small-scale structures such as clusters of galaxies is important (Webster 1985). Therefore, two different effects produced by the cosmological distribution of structures in the universe are expected: a change of the galaxy number count correlated with the mass distribution, namely a magnification bias; and a change of the ellipticity distribution, namely a shear pattern, correlated with the mass distribution as well. Because the expectation values strongly depend on the fraction of non-linear systems and the redshift distribution of the galaxies, it is clear that the analysis of weak lensing effects by large-scale structures is an interesting test of cosmological scenarios.

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