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Astron. Astrophys. 344, 721-734 (1999)

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Gravitational lensing statistics with extragalactic surveys

I. A lower limit on the cosmological constant

Ralf Quast 1 and Phillip Helbig 2

1 Universität Hamburg, Hamburger Sternwarte, Gojenbergsweg 112, D-21029 Hamburg, Germany
2 University of Manchester, Nuffield Radio Astronomy Laboratories, Jodrell Bank, Macclesfield, Cheshire SK11 9DL, England

Received 2 December 1998 / Accepted 14 January 1999


We reanalyse optical gravitational lens surveys from the literature in order to determine relative probabilities in the [FORMULA]-[FORMULA] plane, using a softened singular isothermal sphere lens model. In addition, we examine a portion of the [FORMULA]-[FORMULA] plane which includes all viable cosmological models; this is vital for comparison with other cosmological tests. The results are, within the errors, consistent with those of more specialised analyses, such as those concerning upper limits on [FORMULA] in a flat universe. We note that gravitational lensing statistics can provide a quite robust lower limit on the cosmological constant as well, which could prove important in confirming current claims of a positive cosmological constant. At 95% confidence, our lower and upper limits on [FORMULA], using lens statistics information alone, are respectively -3.17 and 0.3. For a flat universe, these correspond to lower and upper limits on [FORMULA] of respectively -1.09 and 0.65.

Key words: cosmology: observations – cosmology: theory – cosmology: gravitational lensing

Send offprint requests to: R. Quast

Correspondence to: rquast@hs.uni-hamburg.de

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© European Southern Observatory (ESO) 1999

Online publication: March 29, 1999