Gravitational Lensing

In general relativity, the presence of matter (energy density) can curve spacetime, and the path of a light ray will be deflected as a result. This process is called gravitational lensing and in many cases can be described in analogy to the deflection of light by (e.g. glass) lenses in optics. Many useful results for cosmology have come out of using this property of matter and light.

For many of the cases of interest one does not need to fully solve the general relativistic equations of motion for the coupled spacetime and matter, because the bending of spacetime by matter is small. (Quantitatively the matter bending space is moving slowly relative to c, the speed of light and the "gravitational potential" Phi induced by the matter obeys |Phi|/c2 << 1 .)

A sketch of the paradigm of a lensed system is below ( source): In a system where lensing occurs there is a

• source: where the light comes from, can be a quasar, the cosmic microwave background, a galaxy, etc.
• lens(es): which deflect(s) the light by an amount related to its quantity of mass/energy, can be anything with mass/energy
• observer: who sees a different amount of light than otherwise because the lens has bent spacetime and thus the travel paths of the light
• image or images: what the observer sees
The light is not only visible light, but more generally any radiation.
As a consequence of lensing, light rays that would have otherwise not reached the observer are bent from their paths and towards the observer. (Light can also be bent away from an observer but that is not the case of interest.) There are different regimes: strong lensing,weak lensing, and microlensing. The distinction between these regimes depends on the positions of the source, lens and observer, and the mass and shape of the lens (which controls how much light is deflected and where).

Strong Lensing
The most extreme bending of light is when the lens is very massive and the source is close enough to it: in this case light can take different paths to the observer and more than one image of the source will appear. A multiple image is shown at right (source). The first example of a double image was found in 1979, of a quasar. The number of lenses discovered has been used to estimate the volume of space back to the sources. This volume depends strongly on cosmological parameters, in particular the cosmological constant (a classic reference is here).
If the source varies with time, the multiple images will vary with time as well. However, the light doesn't travel the same distance to each image, due to the bending of space. So there will be time delays for the changes in the images. These time delays can be used to calculate the hubble constant H0. A few systems with these time delays have been found and are under study. Much of the subtlety in this work lies with constructing the model of the mass distribution forming the lens (see this review for technical detail).
In some special cases the alignment of the source and the lens will be such that light will be deflected to the observer in an "Einstein ring." Some examples and references can be found here on Wikipedia. More often than a ring, the source may get stretched out and curved, and form a tangential or radial arc. A lot of mass is needed to cause an arc to appear, so that properties of arcs (numbers, size, geometry) can often be used to study massive objects like clusters. One can also, given a set of images, try to reconstruct the lens mass distribution (for an example of reconstructing a cluster as a lens see this technical paper).

Weak Lensing
In many cases the lens is not strong enough to form multiple images or arcs. However, the source can still be distorted: both stretched (shear) and magnified (convergence). If all sources were well known in size and shape, one could just use the shear and convergence to deduce the properties of the lens. However, usually one does not know the intrinsic properties of the sources, but has information about the average properties. The statistics of the sources can then be used to get information about the lens. For instance, galaxies in general aren't perfectly spherical, but if one has a collection of galaxies one doesn't expect them all to be lined up. Thus, if this set of galaxies is lensed, on average, or statistically, there will be some overall shear and/or convergence imposed on the distribution, which will give information about the intervening lens(es).
There is a distribution of galaxies far enough away that can be treated as sources, and thus
clusters nearby can be "weighed" (i.e. have their mass measured) using their lensing. Superclusters have been considered as well. In addition, theories of cosmology predict the distribution of large scale structure, the distribution of matter in the universe. The statistical properties of the large scale structure (e.g. the probability of finding a galaxy at one place when there is another a certain distance away) can also be measured by weak lensing, because the matter will produce shear and convergence in distant sources (which can be galaxies, or the cosmic microwave background, for example). Weak lensing is a useful complement to measures of the distribution of luminous mass such as galaxy surveys. Lensing measures all the mass, in particular the dark matter as well as the luminous matter.

There are ongoing searches to use lensing to find a type of dark matter called MACHOs (massive compact halo objects). Although MACHOs, as dark matter, cannot be seen themselves, if they pass in front of a source (e.g. a star nearby), they can cause the star to become brighter for a while, e.g. days or weeks. This effect has been observed, but determinations of the dark matter are not yet conclusive. Observations are underway by many groups. See these notes by Michael Richmond on Gravitational Microlensing: Searches and Results.

Some web references:
(See also the review at Wikipedia.)

comments to jcohn@berkeley.edu
last updated Dec. 13, 2010.