  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-Lemaitre 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 Omega_0. 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) Mpc/h, 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
Omega_0 varies between 0.3 and 1, quite independent of the value of
Omega_Lambda. For Omega_0 <~ 0.3, the correlation strength increases with
decreasing Omega_0, and it scales approximately linearly with the Hubble
constant h.
