Detection of cosmic magnification with the Sloan Digital Sky Survey

We present an 8 σ detection of cosmic magnification measured by the variation of quasar density due to gravitational lensing by foreground large-scale structure. To make this measurement we used 3800 deg² of photometric observations from the Sloan Digital Sky Survey (SDSS) containing ∼200,000 quasars and 13 million galaxies. Our measurement of the galaxy-quasar cross-correlation function exhibits the amplitude, angular dependence, and change in sign as a function of the slope of the observed quasar number counts that is expected from magnification bias due to weak gravitational lensing. We show that observational uncertainties (stellar contamination, Galactic dust extinction, seeing variations, and errors in the photometric redshifts) are well controlled and do not significantly affect the lensing signal. By weighting the quasars with the number count slope, we combine the cross-correlation of quasars for our full magnitude range and detect the lensing signal at >4 σ in all five SDSS filters. Our measurements of cosmic magnification probe scales ranging from 60 h^-1 kpc to 10 h^-1 Mpc and are in good agreement with theoretical predictions based on the WMAP concordance cosmology. As with galaxy-galaxy lensing, future measurements of cosmic magnification will provide useful constraints on the galaxy-mass power spectrum.