Abstract
The mass function of clusters of galaxies is determined from 400 deg 2 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 σ 8 Ω m 0.6 = 0.33 ± 0.03 (for 0.1 ≲ Ω m ≲ 0.4) or, equivalently, σ 8 = (0.16/Ω m ) 0.6 . The amplitude of this relation is significantly lower than the previous canonical value, implying that either Ω m is lower than previously expected (Ω m = 0.16 if σ 8 = 1) or σ 8 is lower than expected (σ 8 = 0.7 if Ω m = 0.3). The shape of the cluster mass function partially breaks this classic degeneracy. We find best-fit parameters of Ω m = 0.19± 0.07 0.08 and σ 8 = 0.9± 0.2 0.3 . High values of Ω m (≳ 0.4) and low σ 8 (≲ 0.6) are excluded at ≳ 2 σ.