Gravitational Lensing by Large Scale Structures: A Review

TL;DR

This review synthesizes the status of cosmic shear measurements as a probe of the matter distribution, detailing the theoretical framework (convergence, shear, E/B modes), observational estimators, and the role of the Limber approximation and non-linear power spectra. It highlights robust two-point diagnostics, emerging three-point statistics, and initial mappings of the 3D dark matter power spectrum, while stressing limitations from non-linear modeling and PSF systematics. The work demonstrates consistent detections across surveys, enabling constraints on key cosmological parameters and galaxy biasing, and it argues that future wide-area, multi-band, and space-based surveys will unlock tomographic reconstructions of dark matter and tighten dark energy constraints. Overall, the paper frames cosmic shear as a mature, rapidly advancing tool for precision cosmology with substantial potential for cross-validation against CMB and other probes.

Abstract

We review all the cosmic shear results obtained so far, with a critical discussion of the present strengths and weaknesses. We discuss the future prospects and the role cosmic shear could play in a precision cosmology era.

Figures (28)

• Figure 1: A light bundle and two of its rays $\cal L$ and $\cal L'$. ${{1= \hbox{$\bf\xi$}}}(w)$ is the physical diameter distance, which separates the two rays on the sky, viewed from the observer ($w=0$).
• Figure 2: Effect of $\kappa$, $\gamma$ or $\omega$ on the displacement of two test particles $1$ and $2$ located on a test ring (dot-dashed circle) with coordinates $({\rm d}\theta,0)$ and $(0,i{\rm d}\theta)$.
• Figure 3: Illustration of the first order effect of cosmic shear on a circular background galaxy of radius $R_0$. The convergence is an isotropic distortion of the image of the galaxy, while the shear is an anisotropic distortion.
• Figure 4: The left panel is a 3-dimensional mass power spectrum for the linear (dashed) and non-linear (solid, using Smith et al. 2002) regimes when baryons are included. A value of $\Omega_b=0.05$ was used. The right panel shows the induced convergence power spectrum (Eq.\ref{['pofkappa']}) for the two dynamical regimes. Other parameters are $\Omega_{\rm cdm}=0.25, \Omega_\Lambda=0.7, \sigma_8=0.9, h=0.7, z_{\rm source}=0.8$.
• Figure 5: In order to compute the shear variances, the galaxy ellipticities are smoothed within a window (dashed red) of fixed radius $\theta_c$ (left). The shear variance will show up as an excess of galaxy alignment with respect to random orientation. The right panel shows the profile of the two filters one usually consider, top-hat (solid line) and compensated (dashed line). On the left, the axis $(e_t,e_r)$ correspond to the local frame attached to each individual galaxy, on which the galaxy ellipticity components can be projected out to give an estimate of the tangential $\gamma_t$ and radial shear $\gamma_r$.