Cross-correlating the sloan digital sky survey with the microwave sky

While most of the microwave background (CMB) 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-Zeldovich (SZ) effect, the Integrated Sachs-Wolfe (ISW) effect, and weak lensing. This formalism is used to compute the signal-to-noise ratio for cross-correlating these effects with various classes of tracer objects from the SDSS. The anticipated samples of SDSS quasars and galaxies with photometrically determined redshifts are found to 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 Ω₀ as well as the equation of state, w. We find that the ISW cross-correlation gives a poor signal-to-noise ratio using these techniques.