QSO-galaxy correlations due to weak lensing in arbitrary Friedmann-Lemâıtre cosmologies

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-Lemâıtre cosmologies. The non-linear growth of density perturbations is included. Compared to 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)hMpc, 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.