GRAVITATIONAL LENS FREQUENCIES AND THE COSMOLOGICAL CONSTANT - AN EXAMINATION OF AMPLIFICATION BIAS AND GALAXY FORMATION REDSHIFT

Previous investigations into the gravitational lens frequencies in quasar samples suggested that observations do not favour cosmological models with a large value of the cosmological constant. However, this conclusion depends critically on assumptions about the degree of amplification bias and the constant comoving number density of galaxies. We examine amplification bias selection effects under the condition that the darker image must be brighter than the limiting magnitude in the sample and show that the amplification bias selection effects are about five times smaller than the previous estimate. We also estimate the survey depth which is required for the darker image to recover the conventional estimates. This revision makes a cosmological model with a large cosmological constant consistent with observations of gravitational lenses. We also find that, when a model of the distribution of the galaxy formation redshifts is used, the lensing frequency is 15-45 per cent lower than for the case of constant number density of galaxies.