QSO-galaxy correlations induced by weak lensing in arbitrary Friedmann-Lemaitre cosmologies

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Abstract
We calculate the angular cross-correlation function between background QSOs and foreground galaxies induced by the weak lensing effect of large-scale structures. Results are given for arbitrary Friedmann-Lemaître cosmologies. The non-linear growth of density perturbations is included. Compared with the linear growth, the non-linear growth increases the correlation amplitude by about an order of magnitude in an Einstein-de Sitter universe, and by even more for lower Ω0. The dependence of the correlation amplitude on the cosmological parameters strongly depends on the normalization of the power spectrum. The QSO-galaxy cross-correlation function is most sensitive to density structures on scales in the range (1 — 10) h−l Mpc, where the normalization of the power spectrum to the observed cluster abundance appears most appropriate. In that case, the correlation strength changes by less than a factor of ≲2 when Ω0 varies between 0.3 and 1, quite independent of the value of ΩΛ. for Ω0 ≲ 0.3, the correlation strength increases with decreasing Ω0, and it scales approximately linearly with the Hubble constant h.

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