We present a comparison of the SZ cluster counts predicted by the Press-Schechter ( PS ) mass function ( MF ) and the X-ray luminosity function ( XLF ) of clusters .
The employment of the cluster XLF , together with the observationally determined X-ray luminosity ( L _ { X } ) -temperature ( T ) relation , may allow us to estimate the SZ cluster counts in a more realistic manner , although such an empirical approach depends sensitively on our current knowledge of the dynamical properties of intracluster gas and its cosmic evolution .
Using both the non-evolving and evolving XLFs of clusters suggested by X-ray observations , we calculate the expectations for SZ surveys of clusters with X-ray luminosity L _ { X } \geq 3 \times 10 ^ { 44 } erg s ^ { -1 } and L _ { X } \geq 1 \times 10 ^ { 43 } erg s ^ { -1 } in the 0.5 - 2.0 band , respectively .
The non-evolving XLF results in a significant excess of SZ cluster counts at high redshifts as compared with the evolving XLF , while a slightly steeper L _ { X } - T relation than the observed one is needed to reproduce the distributions of SZ clusters predicted by the standard PS formalism .
It is pointed out that uncertainties in the cosmological application of future SZ cluster surveys via the standard PS formalism should be carefully studied .