Sunyaev-Zeldovich fluctuations from spatial correlations between clusters of galaxies

We present angular power spectra of the cosmic microwave background radiati on anisotropy due to fluctuations of the Sunyaev-Zeldovich (SZ) effect thro ugh clusters of galaxies. A contribution from the correlation among cluster s, which has been neglected in previous analyses, is especially focused on. Employing the evolving linear bias factor based on the Press-Schechter for malism, we find that the clustering contribution amounts to 20%-30% of the Poissonian contribution at degree angular scales. If we exclude clusters in the local universe, it even exceeds the Poissonian noise and makes the dom inant contribution to the angular power spectrum. As a concrete example, we demonstrate the subtraction of the ROSAT X-ray and Planck SZ flux-limited cluster samples. It indicates that we should include the clustering effect in the analysis of the SZ fluctuations. We further find that the degree sca le spectra essentially depend upon the normalization of the density fluctua tions, i.e., sigma(8), and the gas mass fraction of the cluster, rather tha n the density parameter of the universe and details of cluster evolution mo dels. Our results show that the SZ fluctuations at the degree scale will pr ovide a possible measure of sigma(8), while the arcminute spectra will prov ide a probe of the cluster evolution. In addition, the clustering spectrum will give us valuable information on the bias at high redshift, if we can d etect it by removing X-ray or SZ luminous clusters.