Arcminute fluctuations in the microwave background from clusters of galaxies
A method for computing arcmin microwave fluctuations produced by Compton scattering of the cosmic background photons by hot electrons in clusters of galaxies is described. Microwave images of the sky for a range of Omega and primordial fluctuation spectral index n are generated which are then 'observed' to determine Delta T/T in precisely the same manner as actual observations to determine if the cluster-induced fluctuations are consistent with the measured upper limit. The geometry used by Uson and Wilkinson (1984) in the NRAO experiment and Readhead et al. (1989) in the OVRO experiment are applied to the simulated images. The 95 percent confidence lower limit for Omega is found to be about 1/10 for n = -1 (which approximates the CDM mass spectrum for clusters), while for n = 0 it is 1/7; for n = +1 the limit is 1/5 if the gas density profile extends to five core radii.