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 g ain additional insights into the physics of the low-redshift universe by cr oss-correlating microwave background maps with template maps produced from the SDSS. We present a formalism for cross-correlating data from the Microw ave Anisotropy Probe (MAP) with the Sloan Survey for the thermal Sunyaev-Ze ldovich (SZ) effect, the Integrated Sachs-Wolfe (ISW) effect, and weak lens ing. This formalism is used to compute the signal-to-noise ratio for cross- correlating these effects with various classes of tracer objects from the S DSS. The anticipated samples of SDSS quasars and galaxies with photometrica lly 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-corr elating weakly lensed quasars with maps of the convergence of the CMB is fo und to give strong constraints on Omega(0) as well as the equation of state , w. We find that the ISW cross-correlation gives a poor signal-to-noise ra tio using these techniques.