Cosmology and the halo occupation distribution from small-scale galaxy clustering in the sloan digital sky survey

We use the projected correlation function w_p(r_p) of a volume-limited subsample of the Sloan Digital Sky Survey (SDSS) main galaxy-redshift catalog to measure the halo occupation distribution (HOD) of the galaxies of the sample. Simultaneously, we allow the cosmology to vary within cosmological constraints imposed by cosmic microwave background experiments in a ACDM model. We find that combining w_p(r_p) for this sample alone with observations by the Wilkinson Microwave Anisotropy Probe (WMAP), Arcminute Cosmology Bolometer Array Receiver (ACBAR), Cosmic Background Imager (CBI), and Very Small Array ( VSA) can provide one of the most precise techniques available to measure cosmological parameters. For a minimal, flat, six-parameter ACDM model with an HOD with three free parameters, we find Ωm = 0.278_-0.027^+0.027, σ8 = 0.812 _-0.027^+0.028, and H₀ = 69.8_-2.6 ^+2.6 km s^-1 Mpc^-1 ; these errors are significantly smaller than from cosmic microwave background (CMB) alone and similar to those obtained by combining CMB with the large-scale galaxy power spectrum assuming scale-independent bias. The corresponding HOD parameters describing the minimum halo mass and the normalization and cutoff of the satellite mean occupation are M_min = (3.03_-0.36 ^+0.36)x 10¹² h^-lM⊙, M1 = (4.58 _-0.60^+0.60)xl0¹³ h^-l M⊙, and k = 4.44_-0.69^+0.51. These HOD parameters thus have small fractional uncertainty when cosmological parameters are allowed to vary within the range permitted by the data. When more parameters are added to the HOD model, the error bars on the HOD parameters increase because of degeneracies, but the error bars on the cosmological parameters do not increase greatly. Similar modeling for other galaxy samples could reduce the statistical errors on these results, while more thorough investigations of the cosmology dependence of nonlinear halo bias and halo mass functions are needed to eliminate remaining systematic uncertainties, which may be comparable to statistical uncertainties.