Gravitational lensing statistics with extragalactic surveys - I. A lower limit on the cosmological constant

We reanalyse optical gravitational lens surveys from the literature in order to determine relative probabilities in the lambda(0)-Omega(0) plane, using a softened singular isothermal sphere lens model. In addition, we examine a portion of the lambda(0)-Omega(0) plane which includes all viable cosmological models; this is vital for comparison with other cosmological tests. The results are, within the errors, consistent with those of more specialised analyses, such as those concerning upper limits on lambda(0) in a flat universe. We note that gravitational lensing statistics can provide a quite robust lower limit on the cosmological constant as well, which could prove important in confirming current claims of a positive cosmological constant. At 95% confidence, our lower and upper limits on lambda(0)-Omega(0), using lens statistics information alone, are respectively -3.17 and 0.3. For a flat universe, these correspond to lower and upper limits on lambda(0) of respectively -1.09 and 0.65.