Do clusters of galaxies affect the spectrum of the microwave background?

The distortion, averaged over the sky, due to the Compton scattering of background photons with electrons in the hot gas in clusters of galaxies is calculated. Using an existing sample of X-ray clusters, various values of the density parameter Omega, and plausible models for cluster evolution, Monte Carlo realizations of the microwave sky are generated. The spatial structure of these simulations shows a network of discrete sources whose properties can be a strong function of both evolution and Omega. The amount of spectral distortion in the models is greatest for models characterized by self-similar cluster evolution in an open universe and is within an order of magnitude of the current upper limits. Thus, improved observational sensitivity must inevitably detect some deviation from a blackbody spectrum.