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Astron. Astrophys. 353, 419-426 (2000)

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Gravitational lensing statistics with extragalactic surveys

IV. Joint constraints on [FORMULA] and [FORMULA] from gravitational lensing statistics and CMB anisotropies

J.F. Macias-Perez 1, P. Helbig 1,2, R. Quast 3, A. Wilkinson 1 and R. Davies 1

1 University of Manchester, Jodrell Bank Observatory, Macclesfield, Cheshire SK11 9DL, UK
2 University of Groningen, Kapteyn Astrononomical Institute, P.O. Box 800, 9700 AV Groningen, The Netherlands
3 University of Hamburg, Hamburg Observatory, Gojenbergsweg 112, 21029 Hamburg, Germany

Received 3 June 1999 / Accepted 20 October 1999


We present constraints on the cosmological constant [FORMULA] and the density parameter [FORMULA] from joint constraints from the analyses of gravitational lensing statistics of the Jodrell Bank-VLA Astrometric Survey (JVAS), optical gravitational lens surveys from the literature and CMB anisotropies. This is the first time that quantitative joint constraints involving lensing statistics and CMB anisotropies have been presented. Within the assumptions made, we achieve very tight constraints on both [FORMULA] and [FORMULA]. These assumptions are cold dark matter models, no tensor components, no reionisation, CMB temperature [FORMULA], number of neutrinos [FORMULA], helium abundance [FORMULA], spectral index [FORMULA], Hubble constant [FORMULA] km s-1 Mpc- 1, baryonic density [FORMULA]. All models were normalised to the COBE data and no closed models ([FORMULA]) were computed. Using the CMB data alone, the best-fit model has [FORMULA] and [FORMULA] and at 99% confidence the lower limit on [FORMULA] is 0.8. Including constraints from gravitational lensing statistics doesn't change this significantly, although it does change the allowed region of parameter space. A universe with [FORMULA] is ruled out for any value of [FORMULA] at better than 99% confidence using the CMB alone. Combined with constraints from lensing statistics, [FORMULA] is also ruled out at better than 99% confidence.

As the region of parameter space allowed by the CMB is, within our assumptions, much smaller than that allowed by lensing statistics, the main result of combining the two is to change the range of parameter space allowed by the CMB along its axis of degeneracy.

Key words: cosmology: gravitational lensing – cosmology: cosmic microwave background – cosmology: theory – cosmology: observations

Send offprint requests to: P. Helbig

Correspondence to: p.helbig@jb.man.ac.uk

© European Southern Observatory (ESO) 2000

Online publication: December 17, 1999