Using gravitational lensing effects to detect and map the distribution of dark matter in the universe.Gravitational lensing is a phenomenon predicted by Einstein's general relativity: massive objects like galaxies or black holes bend the path of light passing near them, acting like a giant lens. When this lensing is caused by dark matter — the invisible substance that outweighs ordinary matter by a factor of five — it distorts the images of background galaxies in characteristic ways. By mapping these distortions, astronomers can trace the distribution of dark matter even though it emits no light. This technique has become a cornerstone of modern cosmology, revealing that dark matter forms a vast cosmic web of filaments and halos around galaxies.
The concept of gravitational lensing was first discussed by Einstein in 1936, but the first observed lens was the 'Twin Quasar' in 1979. Dark matter mapping via weak lensing was pioneered in the 1990s by groups including Anthony Tyson and Yannick Mellier.
Light from a distant galaxy travels in straight lines through empty space, but when it passes through a region with dark matter, the gravitational field curves spacetime. The light follows the curved paths, so the galaxy appears shifted, stretched, or even split into multiple images. The amount of distortion depends on the mass of the dark matter along the line of sight. By measuring the shapes of millions of background galaxies statistically, astronomers can reconstruct the dark matter map — a method called weak lensing. Strong lensing, where a single galaxy is dramatically warped into arcs or rings, provides a more direct but rarer probe.
Gravitational lensing is used to map dark matter distributions in galaxy clusters, measure the expansion rate of the universe, and even detect exoplanets via microlensing events.
The Hubble Space Telescope's most famous deep-field images are actually gravitational lenses — the faint smudges of distant galaxies are magnified and distorted by dark matter in the foreground.
| 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 | Angular radius of the Einstein ring — einstein radius angle radian |
| G | variable | Gravitational constant — gravitational constant cubic metre per kilogram per second squared |
| M | variable | Mass of the lensing object — mass kilogram |
| c | variable | Speed of light in vacuum — speed of light metre per second |
| D_{LS} | variable | Angular diameter distance between lens and source — distance metre |
| D_L | variable | Angular diameter distance from observer to lens — distance metre |
| D_S | variable | Angular diameter distance from observer to source — distance metre |
| \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 |
| C^ell | variable | Angular power spectrum at multipole ell — angular power spectrum |
| z | variable | Redshift — redshift |
| H(z) | variable | Hubble parameter at redshift z — hubble parameter kilometre per second per megaparsec |
| chi(z) | variable | Comoving distance to redshift z — comoving distance metre |
| W(z) | variable | Window function (selection function) at redshift z — window function |
| P(k,z) | variable | Three-dimensional power spectrum at wavenumber k and redshift z — power spectrum cubic metre |
| k | variable | Wavenumber — wavenumber reciprocal metre |
| ell | variable | Multipole moment — multipole moment |
| c | constant | Fundamental constant relating distance and time in relativity — speed of light = 299792458 metre per second |
| ∫ dz | operator | Sum over all redshifts along the line of sight — integral operator |
| M | variable | stellar mass — mass kilogram |
| L | variable | stellar luminosity — luminosity watt |
| M_sun | variable | solar mass — mass kilogram |
| L_sun | variable | solar luminosity — luminosity watt |
| a | constant | empirical slope of the relation — empirical slope = 3.5 |
| b | constant | empirical intercept of the relation — empirical intercept = 0 |
| log10 | operator | base-10 logarithm — logarithm base 10 |
| \Delta t | variable | time delay between images — time delay second |
| D_{\Delta t} | variable | time delay distance — distance metre |
| \Delta\phi | variable | difference in lensing potential — lensing potential difference |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |












