Gravitational lensing in a cold dark matter universe

We investigate gravitational lensing due to mass condensations in a biased cold dark matter (CDM) universe using the Press-Schechter theory with density fluctuation amplitudes taken from previous N-body work. Under the critical assumption that CDM haloes have small core radii, we predict a distribution of image angular separations for high-z lensed quasars with a peak at ∼1 arcsec and a half-width of a factor ∼10. Allowing for selection effects at small angular separations, this in good agreement with the observed separations. The estimated frequency of lensing is somewhat lower than that observed, but the discrepancy can be removed by invoking amplification bias and by making a small upward adjustment to the density fluctuation amplitudes assumed in the CDM model.