4.7 Galactic microlensing4 Lensing Phenomena4.5 Weak/statistical lensing

4.6 Cosmological aspects of (strong) lensing 

Gravitational lenses can be used in two different ways to study the cosmological parameters of the universe. The first is to explore a particular lens system in great detail, determine all possible observational parameters (image positions/brightnesses/shapes; matter/light distribution of lens; time variability etc.) and model both lens and source in as much detail as possible. This way one can in principle determine the amount of dark matter in the lens and - maybe even more importantly - the value of the Hubble constant. A reliable determination of the Hubble constant establishes the extragalactic distance scale, something astronomers have been trying to do for more than 70 years [157].

The second approach is of statistical nature: find out how many (what fraction of) quasars are multiply imaged by gravitationally lensing, determine their separation and redshift distributions [184] and deduce the value of (or limits to) tex2html_wrap_inline2429 - matter in clumps of, say, tex2html_wrap_inline2431 - and to tex2html_wrap_inline2433 - the value of the cosmological constant.

The first approach has already been treated in Section  4.1 . Here we will concentrate on the statistical approach. In order to determine which fraction of a certain group of objects is affected by strong lensing (i.e. multiply imaged), one first needs a well-defined underlying sample. What needs to be done is the following:

  1. Do a systematic study of a sample of high-redshift objects: quasar surveys.
  2. Identify the gravitational lens systems among them.
  3. Determine the relative frequency of lensed objects, the distribution of splitting angles tex2html_wrap_inline2435 as a function of lens and source redshifts tex2html_wrap_inline2437 .
  4. Determine matter content of universe tex2html_wrap_inline2429, typical mass scale tex2html_wrap_inline2441, cosmological constant tex2html_wrap_inline2433, by comparison with theoretical models/simulations.

Since quasars are rare objects and lensing is a relatively rare phenomenon, steps 1 and 2 are quite difficult and time-consuming. Nevertheless, a number of systematic quasar surveys with the goal to find (many) lens systems with well defined selection criteria have been done in the past and others are underway right now (e.g. [34Jump To The Next Citation Point In The Article, 112, 114, 201, 209]).

The largest survey so far, the CLASS survey, has looked at about 7000 radio sources at the moment (the goal is 10000). In total CLASS found 12 new lens systems so far. Interestingly, all the lenses have small separations (tex2html_wrap_inline2445 arcsec), and all lensing galaxies are detected [34, 79]. That leaves little space for a population of dark objects with masses of galaxies or beyond. A detailed discussion of lens surveys and a comparison between optical and radio surveys can be found in [98].

The idea for the determination of the cosmological constant tex2html_wrap_inline2447 from lens statistics is based on the fact that the relative lens probability for multiple imaging increases rapidly with increasing tex2html_wrap_inline2433 (cf. Figure 9 of [36Jump To The Next Citation Point In The Article]). This was first pointed out 1990 [63, 183]. The reason is the fact that the angular diameter distances tex2html_wrap_inline2209, tex2html_wrap_inline2207, tex2html_wrap_inline2211 depend strongly on the cosmological model. And the properties that determine the probability for multiple lensing (i.e. the ``fractional volume'' that is affected by a certain lens) depend on these distances [36]. This can be seen, e.g. when one looks at the critical surface mass density required for multiple imaging (cf. Equation (16Popup Equation)) which depends on the angular diameter distances.

The consequences of lensing studies on the cosmological constant can be summarized as follows. The analyses of the frequency of lensing are based on lens systems found in different optical and radio surveys. The main problem is still the small number of lenses. Depending on the exact selection criteria, only a few lens systems can be included in the analyses. Nevertheless, one can use the existing samples to put limits on the cosmological constant. Two different studies found 95%-confidence limits of tex2html_wrap_inline2457  [99] and tex2html_wrap_inline2459  [113, 152]. This is based on the assumption of a flat universe (tex2html_wrap_inline2461). Investigations on the matter content of the universe from (both ``macro-'' and ``micro-'') lensing generally conclude that the fractional matter in compact form cannot exceed a few percent of the critical density (e.g. [35, 45, 125, 163]).



4.7 Galactic microlensing4 Lensing Phenomena4.5 Weak/statistical lensing

image Gravitational Lensing in Astronomy
Joachim Wambsganss
http://www.livingreviews.org/lrr-1998-12
© Max-Planck-Gesellschaft. ISSN 1433-8351
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