Cosmological parameters and the redshift distribution of gravitational lenses

Phillip Helbig & R. Kayser

For known gravitational lens systems the redshift distribution of the lenses is compared with theoretical expectations for ten thousand Friedmann-Lemaître 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 fro 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.