Measuring Ω/b with Weak Lensing

A correlation between the surface density of foreground galaxies tracing the large-scale structure and the position of distant galaxies and quasars is expected from the magnification bias effect. We show that this foreground-background correlation function wfb can be used as a straightforward and almost model-free method to measure the cosmological ratio Ω/b. For samples with appropriate redshift distributions, wfb ∝ Ω , where δ and g are respectively the foreground dark matter and galaxy surface density fluctuations. Therefore, Ω/b ∝ wfb/w, where w ≡ is the foreground galaxy angular two-point correlation function, b is the biasing factor, and the proportionality factor is independent of the dark matter power spectrum. Simple estimations show that the application of this method to the galaxy and quasar samples generated by the upcoming Sloan Sky Digital Survey will achieve a highly accurate and well-resolved measurement of the ratio Ω/b.