Cross-correlating the Sloan Digital Sky Survey with the Microwave Sky

While most of the microwave background fluctuations on angular scales greater than a few arcminutes were generated at z > 800, the low redshift universe does distort the microwave background. Since the Sloan Digital Sky Survey (SDSS) traces the structures in the low-redshift universe, we can gain additional insights into the physics of the low-redshift universe by cross-correlating microwave background maps with template maps produced from the SDSS. We present a formalism for cross-correlating data from the Microwave Anisotropy Probe (MAP) with the Sloan Survey for the thermal Sunyaev-Zel'dovich (SZ) effect, the Integrated Sachs-Wolfe (ISW) effect, and weak lensing. This formalism is used to compute the signal-to-noise for cross-correlating these effects with various classes of tracer objects from the SDSS. It is found that the anticipated samples of SDSS quasars and galaxies with photometrically-determined redshifts would be good tracers for cross-correlating with the CMB. We find that the SZ-galaxy cross-correlation would give good constraints on pressure fluctuations in supercluster-scale gas. Cross-correlating weakly-lensed quasars with maps of the convergence of the CMB is found to give strong constraints on Omega_0 as well as the equation of state w. We find that the ISW cross-correlation gives poor signal-to-noise using these techniques.