The cluster mass function from early Sloan Digital Sky Survey data: Cosmological implications

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 ₈Ω_m^0.6 = 0.33 ± 0.03 (for 0.1 ≲ Ω_m ≲ 0.4) or, equivalently, σ₈ = (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 σ₈ = 1) or σ₈ is lower than expected (σ₈ = 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 σ₈ = 0.9±_0.2 ^0.3. High values of Ω_m (≳ 0.4) and low σ₈ (≲ 0.6) are excluded at ≳ 2 σ.