EDP Sciences
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Volume 409, Number 2, October II 2003
Page(s) 411 - 421
Section Extragalactic astronomy
DOI http://dx.doi.org/10.1051/0004-6361:20031095

A&A 409, 411-421 (2003)
DOI: 10.1051/0004-6361:20031095

Measuring $\Omega_0$ with higher-order quasar-galaxy correlations induced by weak lensing

B. Ménard1, 2, M. Bartelmann1 and Y. Mellier2, 3

1  Max-Planck-Institut für Astrophysik, PO Box 1317, 85741 Garching, Germany
2  Institut d'Astrophysique de Paris, 98bis Bld. Arago, 75014 Paris, France
3  LERMA, Observatoire de Paris, 61 avenue de l'Observatoire, 75014 Paris, France

(Received 21 August 2002 / Accepted 20 May 2003)

Via the magnification bias, gravitational lensing by large-scale structures causes angular cross-correlations between distant quasars and foreground galaxies on angular scales of arcminutes and above. We investigate the three-point cross-correlation between quasars and galaxy pairs measurable via the second moment of the galaxy counts around quasars and show that it reaches the level of a few per cent on angular scales near one arcminute. Combining two- and three-point correlations, a skewness parameter can be defined which is shown to be virtually independent of the shape and normalisation of the dark-matter power spectrum. If the galaxy bias is linear and deterministic, the skewness depends on the cosmic matter density parameter $\Omega_0$ only; otherwise, it can be used to probe the non-linearity and stochasticity of the bias. We finally estimate the signal-to-noise ratio of a skewness determination and find that a sample of about twenty thousand distant quasars e.g. from the Sloan Digital Sky Survey should suffice for a direct measurement of $\Omega_0$.

Key words: cosmology: gravitational lensing -- cosmology: large-scale structure of Universe

Offprint request: B. Ménard, menard@mpa-garching.mpg.de

© ESO 2003