Weaklensing

Weak lensing, or weak gravitational lensing, refers to the subtle distortion of images of distant galaxies caused by the gravitational field of matter along the line of sight. The induced shape changes are small, typically at the percent level, and require statistical analysis of large samples to detect. By measuring the coherent distortions of many galaxies, weak lensing maps the projected mass distribution, including dark matter, and complements galaxy clustering and cosmic microwave background probes.

In the weak-lensing formalism, light is deflected by a mass distribution, described locally by the Jacobian of the lens mapping. The distortion is encapsulated by the complex shear gamma = gamma1 + i gamma2 and the convergence kappa, which describes isotropic magnification. The observable is the reduced shear g = gamma/(1 - kappa); in the weak limit where kappa is small, g approximately equals gamma. The shear field can be decomposed into E-modes and B-modes, with E-modes containing the true lensing signal and B-modes serving as a diagnostic for systematics.

Weak lensing measurements fall into several categories: cosmic shear, which uses the statistical shear from large-scale structure; galaxy-galaxy lensing, which probes the connection between galaxies and their dark matter halos; and cluster weak lensing, which maps the mass profile of galaxy clusters. Key challenges include accurate shape measurement, correction for the point-spread function, and control of biases, intrinsic alignments, and redshift uncertainties. Methods rely on simulations for calibration and robust PSF modeling.

Large surveys such as DES, KiDS, and HSC, with future missions like Euclid and LSST, aim to deliver high-precision weak-lensing data capable of constraining cosmology, including matter density, the amplitude of fluctuations, dark energy properties, and neutrino masses.