Cross‐correlating Cosmic Microwave Background Radiation Fluctuations with Redshift Surveys: Detecting the Signature of Gravitational Lensing

Density inhomogeneities along the line-of-sight distort fluctuations in thecosmic microwave background. Usually, this effect is thought of as a smallsecond-order effect that mildly alters the statistics of the microwavebackground fluctuations. We show that there is a first-order effect that ispotentially observable if we combine microwave background maps with largeredshift surveys. We introduce a new quantity that measures this lensingeffect, $< T(\delta \theta \cdot \nabla T) >$, where T is the microwavebackground temperature and $\delta \theta$ is the lensing due to matter in theregion probed by the redshift survey. We show that the expected signal is firstorder in the gravitational lensing bending angle, $< (\delta \theta)^2>^{1/2}$, and find that it should be easily detectable, (S/N) $\sim$ 15-35, ifwe combine the Microwave Anisotropy Probe satellite and Sloan Digital SkySurvey data. Measurements of this cross-correlation will directly probe the``bias'' factor, the relationship between fluctuations in mass and fluctuationsin galaxy counts.Comment: 13 pages, 4 postscript figures included; Uses aaspp4.sty (AASTeX v4.0); Accepted for publication in Astrophysical Journal, Part