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 i n the cosmic microwave background. Usually, this effect is thought of as a small second-order effect that mildly alters the statistics of th e microwave background fluctuations. We show that there is a first-ord er effect that is potentially observable if we combine microwave backg round maps with large redshift surveys. We introduce a new quantity th at measures this lensing effect, (T(delta theta.VT)), where T is the m icrowave background temperature and delta theta is the lensing due to matter in the region probed by the redshift survey. We show that the e xpected signal is first order in the gravitational lensing bending ang le, [(delta theta)(2)](1/2), and find that it should be easily detecta ble, signal-to-noise ratio similar to 15-35, if we combine the Microwa ve Anisotropy Probe satellite and Sloan Digital Sky Survey data. Measu rements of this cross-correlation will directly probe the ''bias'' fac tor, i.e., the relationship between fluctuations in mass and fluctuati ons in galaxy counts.