Weak Lensing by Large-Scale Structure

In the remaining chapters, we apply lensing to cases where no single object, such as a galaxy or cluster of galaxies, is responsible for the deflection of light from a background source. Instead, all matter along the line of sight to the source acts collectively as a lens. Comparing large samples of observed galaxy shapes to what we would expect for particular cosmological models allows us to constrain the properties of the universe itself. The first step is to describe the statistical properties of density fluctuations in three dimensions, from which we can infer the statistics of the two-dimensional convergence field relevant for lensing. Linear perturbation theory, in which density fluctuations are assumed to be small, provides a framework for lensing by large-scale structure (Sect. 8.1.1), even though a nonlinear treatment is needed for a quantitative comparison between theory and observation. Such considerations cannot be ignored by the researcher, but they do not substantially affect the basic approach to the subject. (See Sect. 8.1.2 for a flavor of what is involved.) For a given model, whether linear or nonlinear, the correlation function and power spectrum encapsulate much of the statistics of structure formation (Sects. 8.2 and 8.3). The lensed versions of these quantities can be inferred from galaxy shapes, which are distorted by the “cosmic shear” from matter in the foreground (Sect. 8.4). Understanding this phenomenon sets the stage for the applications presented in the final section (Sect. 8.5).