THE SUNYAEV-ZELDOVICH EFFECT AND THE VALUE OF OMEGA(O)

We consider the Sunyaev-Zel'dovich (SZ) effect as a probe of Omega(o): Using a self-consistent modeling of X-ray clusters, we examine the de pendence of both the mean Compton y parameter and the SZ source counts on Omega(o). These quantities increase with decreasing Omega(o) due t o the earlier epoch of structure formation in low-density cosmogonies; the results depend only on the quantity of gas heated to the virial t emperature of collapsed objects and are independent of the spatial dis tribution of the gas in the potential wells. Specifically, we compare two models which reproduce the present-day abundance of clusters - a b iased, critical universe and an unbiased, open model with Omega(o) = 0 .3. We find that the mean y parameter approaches the current FIRAS lim it of y < 2.5 x 10(-5) for the open model, demonstrating the importanc e of improving this limit on spectral distortions, and that the SZ sou rce counts and corresponding redshift distribution differ significantl y between the two cosmogonies; millimeter surveys covering a large are a should thus provide interesting constraints on the density parameter of the Universe and on the evolution of the heated gas fraction in vi rialized objects.