Cluster abundance evolution and the Sunyaev-Zeldovich effect in various cosmological models

The redshift dependence of the observed cluster abundance due to the Sunyaev-Zeldovich Effect (SZE) is studied in various cosmological models including flat and open homogeneous (CDM) models and an inhomogeneous model with a large-scale local void. The Press-Schechter formalism is used to derive the abundance at epochs 0 < z < 2 and the cluster mass limit Mlim is given from a flux limit for SZE. It is shown that SZE is useful for constraining the cosmological model parameters, and the abundance in the inhomogeneous model may be comparable with that in the low-density homogeneous models. The significance of relative difference of abundances in the various models is discussed.