The Cluster Mass Function from Early Sloan Digital Sky Survey Data: Cosmological Implications

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Abstract
The mass function of clusters of galaxies is determined from 400 deg2 of early commissioning imaging data of the Sloan Digital Sky Survey using ~300 clusters in the redshift range z = 0.1-0.2. Clusters are selected using two independent selection methods: a matched filter and a red-sequence color-magnitude technique. The two methods yield consistent results. The cluster mass function is compared with large-scale cosmological simulations. We find a best-fit cluster normalization relation of σ8Ω = 0.33 ± 0.03 (for 0.1 Ωm 0.4) or, equivalently, σ8 = (0.16/Ωm)0.6. The amplitude of this relation is significantly lower than the previous canonical value, implying that either Ωm is lower than previously expected (Ωm = 0.16 if σ8 = 1) or σ8 is lower than expected (σ8 = 0.7 if Ωm = 0.3). The shape of the cluster mass function partially breaks this classic degeneracy. We find best-fit parameters of Ωm = 0.19 ± and σ8 = 0.9 ±. High values of Ωm (0.4) and low σ8 (0.6) are excluded at 2 σ.

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