Weak Gravitational Lensing by Large-Scale Structure

TL;DR

This paper surveys how weak gravitational lensing by large-scale structure—cosmic shear—maps dark matter and constrains cosmology. It details the theory of shear and its relation to the 3D matter power spectrum, outlines two-point and higher-order statistics (notably the shear power spectrum and $E$/$B$-mode decomposition), and discusses how tomographic redshift information can tighten parameter constraints. It reviews current observational detections, their cosmological implications, and the dominant systematic challenges, while outlining the substantial gains expected from future ground- and space-based surveys. The work emphasizes the need for improved nonlinear power-spectrum modeling and robust shear measurement techniques to exploit the full potential of cosmic shear for testing gravity and dark energy.

Abstract

Weak gravitational lensing provides a unique method to map directly the distribution of dark matter in the universe and to measure cosmological parameters. This cosmic-shear technique is based on the measurement of the weak distortions that lensing induces in the shape of background galaxies as photons travel through large-scale structures. This technique is now widely used to measure the mass distribution of galaxy clusters and has recently been detected in random regions of the sky. In this review, we present the theory and observational status of cosmic shear. We describe the principles of weak lensing and the predictions for the shear statistics in favored cosmological models. Next, we review the current measurements of cosmic shear and show how they constrain cosmological parameters. We then describe the prospects offered by upcoming and future cosmic-shear surveys as well as the technical challenges that have to be met for the promises of cosmic shear to be fully realized.

Figures (10)

• Figure 1: Illustration of the effect of weak lensing by large-scale structure. The photon trajectories from distant galaxies ( right) to the observer ( left) are deflected by intervening large-scale structure ( center). This results in coherent distortions in the observed shapes of the galaxies. These distortions, or shears, are on the order of a few percent in amplitude and can be measured to yield a direct map of the distribution of mass in the universe.
• Figure 2: Illustration of the geometrical meaning of the shear $\gamma_{i}$ and of the ellipticity $\epsilon_{i}$. A positive (negative) shear component $\gamma_{1}$ corresponds to an elongation (compression) along the $x$-axis. A positive (negative) value of the shear component $\gamma_{2}$ corresponds to an elongation (compression) along the $x=y$ axis. The ellipticity of an object is defined to vanish if the object is circular ( center). The ellipticity components $\epsilon_{1}$ and $\epsilon_{2}$ correspond to compression and elongations similar to those for the shear components.
• Figure 3: Shear map derived by ray-tracing simulations by Jain, Seljak & White (2000). The size and direction of each line gives the amplitude and position angle of the shear at this location on the sky. The displayed region is $1^{\circ}\times 1^{\circ}$ for an SCDM (Einstein-De Sitter) model. Tangential patterns about the overdensities corresponding to clusters and groups of galaxies are apparent. A more complex network of patterns is also visible outside of these structures. The root-mean-square shear is approximately 2% in this map. (From Jain et al. 2000)
• Figure 4: Shear power spectrum for different cosmological models and for source galaxies at $z_{s}=1$. The SCDM model is COBE normalized and thus has a higher amplitude than the three cluster-normalized models $\Lambda$CDM, OCDM, and $\tau$CDM. The thin dashed line shows the $\Lambda$CDM spectrum for linear evolution of structures. Notice that for $l > 1000$ (corresponding approximately to angular scales $\theta < 10'$) the lensing power spectrum is dominated by nonlinear structures.
• Figure 5: Example of an deep image in the cosmic-shear survey by Bacon, Refregier & Ellis (2000). This corresponds to a 1 h exposure with the EEV camera on the William Herschel Telescope (WHT). The field of view is $8'\times 16'$ and achieves a magnitude depth of $R\simeq26$ (5$\sigma$ detection). The bright objects are saturated stars. The faint objects comprise approximately 200 stars and approximately 2000 galaxies that are usable for the weak-lensing analysis. (From Bacon, Refregier & Ellis 2000)