Using light bending by gravity to measure cosmic structures and infer properties like dark matter distribution.Gravitational lensing analysis uses the bending of light by massive objects to map the distribution of matter in the universe, including dark matter. When light from distant galaxies passes near a massive foreground object, its path is curved, creating distorted, magnified, or multiple images. By analyzing these distortions, astronomers can infer the mass distribution of the lensing object, even if that mass is invisible, such as dark matter.
The theory of gravitational lensing was first derived by Einstein in 1936, but the first complete gravitational lens was discovered in 1979. Weak lensing became a major cosmological tool in the 1990s and 2000s.
The gravitational field of a massive object acts like a lens, deflecting light rays according to general relativity. In strong lensing, this produces dramatic effects like Einstein rings and multiple images. In weak lensing, the distortion is subtle, but by statistically analyzing the shapes of many background galaxies, astronomers can map the dark matter distribution. The degree of distortion depends on the mass and distance of the lens, allowing precise measurements of cosmic structure.
Gravitational lensing is used to map dark matter in galaxy clusters, measure the expansion rate of the universe, and detect exoplanets via microlensing. It also helps test modified gravity theories.
A single galaxy cluster can act as a gravitational lens, producing multiple images of the same background galaxy, sometimes arranged in a near-perfect Einstein ring.
| β | variable | ratio of angular diameter distances — distance ratio |
| D_ds | variable | angular diameter distance from lens to source — angular diameter distance metre |
| D_s' | variable | angular diameter distance from observer to source in a reference cosmology — angular diameter distance metre |
| D_ds' | variable | angular diameter distance from lens to source in a reference cosmology — angular diameter distance metre |
| D_s | variable | angular diameter distance from observer to source — angular diameter distance metre |
| \theta_E | variable | Einstein ring angular radius — angle radian |
| M | variable | Mass of the lensing object — mass kilogram |
| D_{\rm LS} | variable | Angular diameter distance from lens to source — distance metre |
| D_{\rm L} | variable | Angular diameter distance from observer to lens — distance metre |
| D_{\rm S} | variable | Angular diameter distance from observer to source — distance metre |
| G | constant | Universal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| \sqrt{} | operator | Takes the square root of the argument — square root |
| N | variable | number of objects — number of objects |
| L | variable | luminosity of objects — luminosity watt |
| α | variable | power-law index (slope) — power law index |
| d/dL | operator | differentiation with respect to luminosity — derivative with respect to luminosity |












