Annu. Rev. Astron. Astrophys. 1999. 37: 127-189
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Although the use of weak lensing analysis and its applications in cosmology made spectacular progress during the last five years, most of the astrophysical questions addressed by Fort & Mellier (1994) in their conclusions are still pending. However, it seems that we are progressing quickly in the right direction, even if some of these problems are complex and should be envisioned in a long-term perspective.

The HST images have dominated most of the results, in particular in the modeling of clusters of galaxies. Thanks to the formidable work devoted to mass reconstruction, the projected mass density of clusters of galaxies are now robust and reliable. It is now important to couple strong and weak lensing features (Seitz et al 1998, AbdelSalam et al 1998b, Dye & Taylor 1998, Van Kampen 1998) in order to build consistent models for clusters. It is worth noting that for many of the issues discussed in this review, it was emphasized that precise and reliable mass reconstructions of clusters of galaxies are crucial and determine the reliability of many scientific outcomes. In this respect, it is important to keep in mind that the redshift distribution of the sources is indispensable and that the new giant telescopes will be the best tools for this purpose.

From the sample of clusters already analyzed, there are converging results that Omega < 0.3 with a high confidence level. However, complete cluster samples are necessary for deeper investigations of cluster properties. They should come out rapidly from weak lensing studies of ROSAT samples (Rosati 1999). Indeed, we now have a very good understanding of the mass distribution of each component (dark matter, hot gas, galaxies) in clusters of galaxies and we are close to understanding the discrepancy between the lensing mass and the X-ray mass of clusters. During the next five years, one can reasonably expect significant improvements in our knowledge of the dynamics of clusters of galaxies by jointly using weak lensing reconstruction, from HST and giant telescopes images, and a full description of the hot gas, from AXAF and XMM observations.

In contrast, the investigation of galaxy halos from galaxy-galaxy lensing is still in its infancy and the preliminary results presented in this review must be confirmed. A new generation of instruments will contribute to the development of this hot topic. Below 10 arcseconds down to 2 arcseconds, "wide field" HST observations with the new Advanced Camera devoted to deep galaxy-galaxy lensing studies appear to be a promising approach. Beyond this scale, the high image quality of telescopes like Keck, GEMINI, Subaru, Magellan, the VLT or CFHT will be decisive in obtaining valuable constraints from galaxy-galaxy lensing analysis between 10 and 60 arcseconds.

Parallel to these studies, we can now envision fully exploiting some of the most valuable information that gravitational lensing can provide, namely the relation(s) between light and mass distributions in the universe. Theoretical studies have demonstrated that in the near future the weak lensing analysis coupled with the study of the galaxy distribution will allow us to understand the evolution of the biasing factor with scale and redshift. However, it is important to explore the case of non-linear and stochastic biasing in order to understand which parameters can be reasonably constrained. The possible existence of large dark halos around galaxies or in clusters of galaxies is also an unknown but fascinating topic. In this respect, the dark cluster candidates discussed by Hattori et al (1997), Erben et al (1999), or the remarkable distortion field detected by Bonnet et al (1994) in the periphery of Cl0024+1654, which does not seem to be correlated to luminous matter, deserves more careful investigation.

The study of the contents and the past history of galaxies made formidable progress as well. It is clear that jointly using the magnification of cluster-lenses with the unprecedented image quality of HST, or with the wide field and high sensitivity of SCUBA, results in highly competitive tools. In the future, continuous developments are expected, but the observation of extremely high redshift galaxies which could not be observed without magnification is certainly a major goal, in particular in the submillimeter wavebands. As demonstrated by the recent study of Soifer et al (1998), the coming of optical and near-infrared spectroscopic capabilities on the giant telescopes will permit one to study in detail their spectral energy distribution and the kinematics of their stellar and gas components. The magnification permits the viewing of a huge amount of detail on the images of these galaxies, and we can envision probing small details of these galaxies from image reconstruction "à la Kochanek" (Kochanek et al 1989). Unfortunately, though theoretical tools have been developed in order to recover the morphology of these lensed galaxies, the quality of optical and submillimeter data are not good enough to produce reliable details of the sources from inversion. This is probably a goal for the Large Southern Array (LSA) which will have much better sensitivity and resolution.

With new instruments, such as Megacam at CFHT (Boulade et al 1998) or the VST at the European Southern Observatory (Arnaboldi et al 1999) in Paranal, we are now entering the era of wide field subarcsecond imaging surveys which will produce the first shear-limited samples or, similarly, the first mass selected catalogues of gravitational condensations (Reblinsky & Bartelmann 1999). Their designs are optimized to investigate weak lensing induced by large-scale structures in order to produce the first mass maps of the universe. They will permit recovering of the detailed spectrum of the projected power spectrum of mass density fluctuations as well as measuring (Omega, lambda) with an accuracy greater than 10% (see Figure 13, color). There are still some theoretical issues (see Sections 3.3 and 4.4) that must be addressed in detail from both the theoretical and simulation points of view. For most of them, there are no crucial conceptual difficulties, so they should be fixed rapidly. On the other hand, the control of systematics which can affect weak lensing measurement, as well as the correction for an anisotropic PSF, could be critical and should be considered seriously in the future for very low shear amplitudes (< 1%). Nevertheless, these cameras, as well as the very wide field surveys of the VLA-FIRST and the SDSS, should provide a major breakthrough in weak lensing applications for cosmology.

In the longer term, after the crucial results expected for mass maps with wide-field CCD cameras, the New Generation Space Telescope (NGST) and Planck Surveyor could be ultimate steps in this area. The potential interest of NGST for weak lensing has been summarized by Schneider & Kneib (1999), who argued that low-mass clusters and groups of galaxies as well as very distant clusters should be detectable with this telescope. In parallel, as reported by Stompor & Efstathiou (1999) and Metcalf & Silk (1998), weak lensing on the CMB should be able to break the geometrical degeneracy and ultimately provide the (Omega, lambda) parameters. This coupling between observations of CMB fluctuations and weak lensing analyses emerges as a consecration illustrating the major roles played by these two complementary approaches to present-day cosmology.


I am particularly grateful to B. Fort for his advices, and his friendly and continuous encouragements during the long period of preparation of the review. I would like to thank first F Bernardeau, F Casoli, S Charlot, R Ellis, P Schneider and L Van Waerbeke for their careful reading and useful comments of the manuscript as well as for their strong support during its writing. I thank all the other close collaborators who participate to our gravitational lensing projects, and the colleagues with whom we had many fruitful discussions, namely M Bartelmann, H Bonnet, T Broadhurst, J-C Cuillandre, T Erben, H Hoekstra, B Jain, N Kaiser, J-P Kneib, C Kochanek, J-F Le Borgne, P-Y Longaretti, G Luppino, D Narasimha, R Pelló, M Pierre, C Seitz, S Seitz, U Seljak, I Smail, G Soucail and G Squires. I thank I Gioia for providing me data prior to publication, and T Brainerd, B Jain, P Schneider and G Squires, for giving me their authorization to publish figures of their papers in this review. I thank especially M Dantel-Fort for her assistance and also for the crucial work she does in order to have all these data set ready for our scientific objectives. Part of this work was supported by the Programme National de Cosmologie which is funded by the Centre National de la Recherche Scientifique, the Commissariat à l'énergie Atomique and the Centre National d'études Spatiales, under the responsibility of the Institut National des Sciences de l'Univers and the Indo-French Centre for the Promotion of Advanced Research IFCPAR grant 1410-2.

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