|Annu. Rev. Astron. Astrophys. 1999. 37:
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The potential of gravitational lensing for cosmography, already discussed by Blandford & Narayan (1992), Fort & Mellier (1994) for the particular cases of arc(let)s, is clear but also challenging. The increasing evidence that the whole set of observations are compatible with a non-zero cosmological constant, for instance, motivated many new studies devoted to the constraints on , following the early suggestions by Paczynski & Gorski (1981). One of the most promising and reliable approaches explored by recent theoretical studies has been raised by Bernardeau et al (1997), Van Waerbeke et al (1999). These works clearly demonstrate that the determination of the cosmological parameters (0, ) using future surveys of weak lensing induced by large-scale structures should provide with a high accuracy (see Figure 7 and Figure 13). Since this was already pointed out in Section 4.1, I do not discuss it in more detail here. In the following sections, I focus on new and more speculative investigations, which are still difficult to implement but seem promising in the future.
Figure 13. Constraints on (, ) from a weak lensing survey covering 10 × 10 square-degrees. The bright and dark regions refer to 1 and 2 level. The left strip is for an = 0.3 universe, and the right band for an = 1 universe. The solid and dot-dashed lines correspond to a zero-curvature universe and to a fixed deceleration parameter, respectively (from Van Waerbeke et al 1999).