The Deltatheta-z_s relation for gravitational lenses as a cosmological test

Recently, Park & Gott claimed that there is a statistically significant, strong, negative correlation between the image separation Deltatheta and source redshift z_s for gravitational lenses. This is somewhat puzzling if one believes in a flat (k=0) universe, since in this case the typical image separation is expected to be independent of the source redshift, while one expects a negative correlation in a k=-1 universe and a positive one in a k=+1 universe. Park & Gott explored several effects that could cause the observed correlation, but no combination of these can explain the observations with a realistic scenario. Here, I explore this test further in three ways. First, I show that in an inhomogeneous universe a negative correlation is expected regardless of the value of k. Secondly, I test whether the Deltatheta-z_s relation can be used as a test to determine lambda_0 and Omega_0, rather than just the sign of k. Thirdly, I compare the results of the test from the Park & Gott sample with those using other samples of gravitational lenses, which can illuminate (unknown) selection effects and probe the usefulness of the Deltatheta-z_s relation as a cosmological test.