Cosmological parameters and the redshift distribution of gravitational lenses

Abstract

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~$m_{\rm lim}$, 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 $\Omega_{0}$ 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.