Measuring the Mach number of the universe via the Sunyaev-Zel'dovich effect

The cross-correlating cosmic microwave background (CMB) fluctuations caused by the Sunyaev-Zel'dovich effect from observed clusters of galaxies with their redshifts can be used to measure the mean squared cluster peculiar velocity with an error σ_CS²≃ (300 km/s)². This can be done around z>0.3 with clusters of flux above 200 mJy which will be detected by PLANCK, coupled with high resolution microwave images to eliminate the cosmological part of the CMB fluctuations. The latter can be achieved with observations by the planned ALMA array or the NSF South Pole telescope and other surveys. By measuring the rms peculiar velocity of clusters and their bulk flow in, e.g., 4 spheres of ∼ 100h^-1 Mpc at z=0.3, we could have a direct measurement of the matter density 0.21<Ω_m<0.47 at 95% confidence level.