Cross‐Correlating the Sloan Digital Sky Survey with the Microwave Sky

While most of the microwave background fluctuations on angular scales greaterthan a few arcminutes were generated at z > 800, the low redshift universe doesdistort the microwave background. Since the Sloan Digital Sky Survey (SDSS)traces the structures in the low-redshift universe, we can gain additionalinsights into the physics of the low-redshift universe by cross-correlatingmicrowave background maps with template maps produced from the SDSS. We presenta formalism for cross-correlating data from the Microwave Anisotropy Probe(MAP) with the Sloan Survey for the thermal Sunyaev-Zel'dovich (SZ) effect, theIntegrated Sachs-Wolfe (ISW) effect, and weak lensing. This formalism is usedto compute the signal-to-noise for cross-correlating these effects with variousclasses of tracer objects from the SDSS. It is found that the anticipatedsamples of SDSS quasars and galaxies with photometrically-determined redshiftswould be good tracers for cross-correlating with the CMB. We find that theSZ-galaxy cross-correlation would give good constraints on pressurefluctuations in supercluster-scale gas. Cross-correlating weakly-lensed quasarswith maps of the convergence of the CMB is found to give strong constraints onOmega_0 as well as the equation of state w. We find that the ISWcross-correlation gives poor signal-to-noise using these techniques.Comment: 23 pages; 3 PS figures; Version accepted by Ap