Cluster abundances and S-Z power spectra: effects of non-Gaussianity and early dark energy

In the standard Lambda CDM cosmological model with a Gaussian primordial density fluctuation field, the relatively low value of the mass variance parameter (sigma_8=0.74{+0.05}{-0.06}, obtained from the WMAP 3-year data) results in a reduced likelihood that the measured level of CMB anisotropy on the scales of clusters is due to the Sunyaev-Zeldovich (S-Z) effect. To assess the feasibility of producing higher levels of S-Z power, we explore two alternative models which predict higher cluster abundance. In the first model the primordial density field has a chi^2_1 distribution, whereas in the second an early dark energy component gives rise to the desired higher cluster abundance. We carry out the necessary detailed calculations of the levels of S-Z power spectra, cluster number counts, and angular 2-point correlation function of clusters, and compare (in a self-consistent way) their predicted redshift distributions. Our results provide a sufficient basis upon which the viability of the three models may be tested by future high quality measurements.