Cosmological parameters and the redshift distribution of gravitational lenses

For known gravitational lens systems the redshift distribution of the lenses is compared with theoretical expectations for ${10}^4$~Friedmann-Lema^\i tre~cosmological models, which more than cover the range of possible cases. The comparison is used for assigning a relative probability to each of the models. The entire procedure is repeated for different values of the inhomogeneity parameter~$\eta$ and the limiting spectroscopic magnitude~$m_{\mathrm{l}\mathrm{i}\mathrm{m}}$, which is important for selection effects. The dependence on these two parameters is examined in more detail for the special cases~${\lambda }_0=0$ and $k=0$. Previous results that this method is a better probe for~${\lambda }_0$ than ${\mathrm{\Omega }}_0$ are confirmed, but it appears that the low probability of models with large~${\lambda }_0$~values found using similar methods is due to a selection effect. The power of this method to discriminate between cosmological models can of course be improved if more gravitational lens systems are found. However, our numerical simulations indicate that a reasonable number of observed systems cannot deliver interesting constraints on the cosmological parameters.